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High SchoolAP StatsSki lii
Hayward CornmunitySchool District715-634-2619
#HurricaneStrongMade with PasterMyWall corn
AP Statistics Exam Review Course
eek 1 Checklist
Unit 1: One Variable DataD Watch and take notes on Video 1.1 Types of DisplaysD Watch and take notes on Video 1 .2 Describing a DistributionD Complete 2015 Free Response Question #1 and score using videoD Complete Unit 1 Practice Multiple Choice
Complete and score Unit 1 Practice Free Response Question
Unit 2: Two Variable DataD Watch and take notes on Video 2.1 Describing a RelationshipD Watch and take notes on Video 2.2 Predictions and ResidualsE1 Complete 2017 Free Response Question #1 and score using videoD Complete Unit 2 Practice Multiple ChoiceEl Complete and score Unit 2 Practice Free Response Question
Unit 3: Sampling and ExperimentsEl Watch and take notes on Video 3.1 Sampling Methods and IssuesEl Watch and take notes on Video 3.2 Experimental DesignEl Complete 2016 Free Response Question #3 and score using videoEl Complete Unit 3 Practice Multiple ChoiceEl Complete and score Unit 3 Practice Free Response Question
Week 1 Track Your Progress
Practice Multiple Choice Score Practice Free Response Question Score
Unit 1 (out of 10) Unit 1 (out of 4)
Unit 2 (out of 10) Unit 2 (out of 4)
Unit 3 (out of 10) Unit 3 (out of 4)
4. STATS MEDIC
L••-
— .
Week 2 Checklist
Unit 4: Probability
D Watch and take notes on Video 4.1 General Probability
D Watch and take notes on Video 4.2 Binomial Distributions
E1 Watch and take notes on Video 4.3 Transforming and Combining Random Variables
D Watch and take notes on Video 4.4 Normal Distribution Calculations
D Watch and take notes on Video 4.5 Geometric Distributions
D Complete 2017 Free Response Question #3 and score using video
D Complete Unit 4 Practice Multiple Choice
D Complete and score Unit 4 Practice Free Response Question
Unit 5: Sampling Distributions
U Watch and take notes on Video 5.1 Introduction to Sampling Distributions
U Watch and take notes on Video 5.2 Sampling Distributions for One Population
U Watch and take notes on Video 5.3 Sampling Distributions for Two Populations
U Complete 2010 Free Response Question #2 and score using video
U Complete Unit 5 Practice Multiple Choice
U Complete and score Unit 5 Practice Free Response Question
Unit 6: Confidence Intervals
U Watch and take notes on Video 6.1 One Sample Confidence Intervals
U Watch and take notes on Video 6.2 Two Sample Confidence Intervals
U Complete 2017 Free Response Question #2 and score using video
U Complete Unit 6 Practice Multiple Choice
U Complete and score Unit 6 Practice Free Response Question
Week 2 Track Your Progress
Practice Multiple Choice Score Practice Free Response Question Score
Unit 4 (out of 20) Unit 4 (out of 4)
Unit 5 (out of 10) Unit 5 (out of 4)
Unit 6(out of 20) Unitó(out of 4)
.+ STATS MEDIC
j..
...................—.........
Week 3 Checklist
6nit 7: Significance TestsD Watch and take notes on Video 7.1 One Sample Significance TestsEJ Watch and take notes on Video 7.2 Two Sample Significance TestE Watch and take notes on Video 7.3 Difference of Means or Mean of Differences?D Watch and take notes on Video 7.4 Chi-square Tests
Watch and take notes on Video 7.5 Inference for Linear RegressionD Watch and take notes on Video 7.6 Type I and Type II Errors + PowerE1 Complete 2015 Free Response Question #4 and score using videoE Complete 2017 Free Response Question #5 and score using videoEJ Complete Unit 7 Practice Multiple ChoiceE Complete and score Unit 7 Practice Free Response Question
Getting Ready for the AP Exam!E Watch and take notes on Video: Name That Significance TestU Watch and take notes on Video: Using Your Calculator on the AP Stats ExamU Watch and take notes on Video: Know Your AP Stats Formula SheetU Watch and take notes on Video: How to CRUSH the AP Stats Free ResponseU Watch and take notes on Video: How to Survive the Investigative TaskU Watch and take notes on Video: Top 10 AP Stats Exam Tips
Full Length Practice ExamU Complete the Practice Exam Multiple Choice QuestionsU Complete the Practice Exam Free Response QuestionsU Grade the Practice Exam
Week 3 Track Your Progress
Practice Multiple Choice Score Practice Free Response Question Score
LUnit 7 (out of 20) Unit 7 (out of 4)
.1. STATS MEDIC
Practice Exam
Section I Multiple Choice
Number correct(out of 40)
x 1.2500=Section I Score
Section II Free Response
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
(out of 4)
(outof4)
(outof4)
(out of 4)
(outof4)
(outof4)
xl.8750 =
_________
xl.8750 =
________
xl.8750 =
_________
xl.8750 =
_________
xl.8750 =
________
x3.1250
_________
Sum =
Section H Score
.
Section I Score+
Section II Score Composite Score
4’ STATS MEDIC
.
Composite Score
Composite Score AP Score]
70—100 5
57—69 4
44—56 3
33—43 2
0—32 1
Stats Medic AP Stats Exam Review — Videos and Practice Problems
Unit 1: One Variable Data1 .1 Types of Displays Unit 1 Stats Medic Practice Multiple Choice (10)
1 .2 Describing a Distribution Unit 1 Stats Medic Practice Free Response
Unit 1 AP Free Response (2015 #1)
Unit 2: Two Variable Data2.1 Describing a Relationship Unit 2 Stats Medic Practice Multiple Choice (10)
2.2 Predictions and Residuals Unit 2 Stats Medic Practice Free Response
Unit 2 AP Free Response (2017 #1)
Unit 3: Sampling and Experiments3.1 Sampling Methods and Issues Unit 3 Stats Medic Practice Multiple Choice (10)
3.2 Experimental Design Unit 3 Stats Medic Practice Free Response
Unit 3 AP Free Response (2016 #3)
Unit 4: Probability4.1 General Probability Unit 4 Stats Medic Practice Multiple Choice (20)
4.2 Binomial Distributions Unit 4 Stats Medic Practice Free Response
4.3 Transforming and Combining Random Variables Unit 4 AP Free Response (2017 #3)
4.4 Normal Distribution Calculations
4.5 Geometric Distributions
Unit 5: Sampling Distributions5.1 Introduction to Sampling Distributions Unit 5 Stats Medic Practice Multiple Choice (10)
5.2 Sampling Distributions for One Population Unit 5 Stats Medic Practice Free Response
5.3 Sampling Distributions for Two Populations Unit 5 AP Free Response (2010 #2)
Unit 6: Confidence Intervals6.1 One Sample Confidence Intervals Unit 6 Stats Medic Practice Multiple Choice (20)
6.2 Two Sample Confidence Intervals Unit 6 Stats Medic Practice Free Response
Unit 6 AP Free Response (2017 #2)
Unit 7: Significance Tests7.1 One Sample Significance Tests Unit 7 Stats Medic Practice Multiple Choice (20)7.2 Two Sample Significance Tests Unit 7 Stats Medic Practice Free Response
7.3 Difference of Means OR Mean of Differences? Unit 7 AP Free Response (2015 #4)
7.4 Chi-square Tests Unit 7 AP Free Response (201 7 #5)
7.5 Inference for Linear Regression
7.6 Type 1 and Type 2 Errors + Power
+ STATS MEDIC
Getting Ready for the AP Exam! .
4’ STATS MEDIC
Name That Significance Test Stats Medic Full Length Practice Exam
Using Your Calculator on the AP Stats Exam Multiple Choice (40)
Know Your AP Stats Formula Sheet Free Response (6)
How to CRUSH the AP Stats Free Response
How to Survive the Investigative Task
Top 10 AP Stats Exam Tips
.1.
Stat
sM
edic
AP
Exam
Rev
iew
Cou
rse
—D
iagn
ostic
Tes
t
1.A
coll
ege
prof
esso
rco
nduc
ted
asu
rvey
inor
der
toas
sess
how
muc
hm
oney
nurs
ing
maj
ors
spen
don
cour
sem
ater
ial
com
pare
dto
all
othe
rm
ajor
s.T
odo
so,
she
sele
cted
ara
ndom
sam
ple
of34
stud
ents
.E
ach
stud
ent
was
clas
sifi
edas
anu
rsin
gm
ajor
oras
ano
n-nu
rsin
gm
ajor
.T
hey
wer
eth
enas
ked
how
muc
hth
eysp
ent
onbo
oks
and
othe
rm
ater
ials
requ
ired
for
thei
rco
urse
sth
isse
mes
ter.
Her
ear
epa
ralle
lbo
xplo
tssu
mm
ariz
ing
the
resp
onse
s:
Bas
edup
onth
ebo
xplo
ts,
whi
chof
the
follo
win
gst
atem
ents
cann
otbe
conc
lude
d?(A
)T
hera
nge
ofth
edi
stri
buti
onof
the
cost
ofco
urse
mat
eria
lsfo
rnu
rsin
gm
ajor
sis
abou
tth
esa
me
asth
atof
non-
nurs
ing
maj
ors.
(B)
The
max
imum
cost
for
non-
nurs
ing
maj
ors
isgr
eate
rth
anth
em
edia
nco
stfo
rnu
rsin
gm
ajor
s.(C
)T
heva
riab
ility
ofth
eco
stof
cour
sem
ater
ials
for
the
mid
dle
50%
ofnu
rsin
gm
ajor
sis
grea
ter
than
the
vari
abili
tyof
the
mid
dle
50%
for
non-
nurs
ing
maj
ors.
(D)
The
med
ian
cost
ofco
urse
mat
eria
lsfo
rnu
rsin
gm
ajor
sis
over
$300
mor
eth
anth
em
edia
nco
stof
cour
sem
ater
ials
for
non-
nurs
ing
maj
ors.
(E)
The
boxp
lots
reve
alth
at17
stud
ents
are
nurs
ing
maj
ors
and
17st
uden
tsar
eno
n-nu
rsin
gm
ajor
s.
2.In
orde
rto
com
pare
the
real
esta
tem
arke
tsin
Pitts
burg
han
dPh
ilade
lphi
a,a
real
tor
sele
cted
ara
ndom
sam
ple
of15
0ho
mes
inth
eP
itts
burg
har
eaan
d10
0ho
mes
inth
ePh
ilade
lphi
aar
ea.
Show
nbe
low
are
dotp
lots
show
ing
the
dist
ribu
tion
ofho
me
pric
efo
rth
eho
mes
inth
ese
two
citie
s.
iJb
+P
itts
burg
h10
020
030
0400
500
600
700
800
900
1000
hI
SP
hila
delp
hia
100
200
300
400
500
600
700
800
900
1000
Hom
eP
rice
(in
thou
sand
s)
The
mea
nho
me
pric
efo
rbo
thci
ties
isap
prox
imat
ely
$500
000.
The
stan
dard
devi
atio
nof
hom
epr
ice
for
one
city
is$1
00,7
40an
dth
eot
her
is$2
67,2
10.
Whi
chof
the
follo
win
ggi
ves
the
corr
ect
valu
ean
din
terp
reta
tion
ofth
est
anda
rdde
viat
ion
ofth
eho
me
pric
esfo
rho
mes
inth
eP
itts
burg
har
ea?
(A)
The
pric
eof
hom
esin
the
Pit
tsbu
rgh
sam
ple
are
with
in$1
00,7
40of
the
mea
nho
me
pric
eof
$500
,000
.(B
)In
the
sam
ple
ofho
mes
from
Pit
tsbu
rgh,
mos
tof
the
hom
epr
ices
are
atle
ast
$100
,740
abov
eor
belo
wth
em
ean
hom
epr
ice
of$5
00,0
00.
(C)
The
pric
eof
the
hom
esin
the
Pitts
burg
hsa
mpl
ety
pica
llyva
ryby
abou
t$2
67,2
10fr
omth
em
ean
hom
epr
ice
of$5
00,0
00.
(D)
Inth
esa
mpl
eof
hom
esfr
omP
itts
burg
h,th
em
iddl
e50
%of
hom
epr
ices
are
with
in$2
67,2
10of
the
mea
nho
me
pric
eof
$500
,000
.(E
)T
hepr
ice
ofho
mes
inth
eP
itts
burg
hsa
mpl
ear
e$1
00,7
40fr
omth
em
ean
hom
epr
ice
of$5
00,0
00.
I[—1
Xsr
smg
•N
on-N
ursi
ngM
ajor
s
200
300
400
500
600
00
Cos
tof
Cou
rse
Mat
eria
l
+ST
ATS
MED
IC4.
STAT
SM
EDIC
3.T
hese
gm
ente
dba
rgr
aph
show
sho
wm
any
ofth
efi
rst
44U
nite
dS
tate
sP
resi
dent
sha
vedi
ed
whi
lein
offi
ce,
clas
sifi
edby
polit
ical
part
y.W
hat
prop
orti
onof
thes
eP
resi
dent
sha
vedi
ed
whi
lein
offi
ce?
100% 90
%
80%
70%
160
%
50%
40%
30%
20%
10% 0%
(A)
0.04
5
(B)
0.08
0
(C)
0.09
1
(D)0
.182
(E)
0.66
2
4.A
groc
ery
stor
em
anag
erw
ants
toes
tim
ate
the
mea
npu
rcha
seto
tal
for
all
cust
omer
sth
at
shop
athe
rst
ore.
To
doso
,sh
ese
lect
sa
rand
omsa
mpl
eof
30re
ceip
tsfr
omth
ela
rge
listo
f
all
rece
ipts
that
are
stor
edin
the
com
pute
r.H
ere
isa
do
tplo
tof
the
resu
lts.
.--I
010
020
030
040
050
0Pu
Icha
8cTo
tal (
$)
The
mea
npu
rcha
seto
tal
is$9
3.80
and
the
med
ian
purc
hase
tota
lis
$75.
80.
The
stor
e
man
ager
inve
stig
ates
and
lear
nsth
atth
ecu
stom
erth
atm
ade
a$5
00pu
rcha
seha
dno
t
purc
hase
dgr
ocer
ies,
but
rath
era
$5
00
gift
card
.B
ecau
seth
iscu
stom
er’s
purc
hase
was
not
typi
cal,
the
man
ager
deci
des
toex
clud
eth
isto
tal
from
the
data
set.
How
will
rem
ovin
gth
e
$500
purc
hase
from
the
data
set
affe
ctth
eva
lue
ofth
em
ean
and
the
med
ian?
(A)
The
mea
nw
illd
ecre
ase
mor
eth
anth
em
edia
n.
(B)
The
mea
nw
illde
crea
sele
ssth
anth
em
edia
n.
(C)
The
mea
nw
illst
ayth
esa
me,
but
the
med
ian
will
decr
ease
.
(D)
The
mea
nw
illin
crea
sem
ore
than
the
med
ian.
(E)
The
mea
nw
illin
crea
se,
but
not
asm
uch
asth
em
edia
n.
5.W
hen
hom
eow
ners
list
thei
rho
me
for
sale
,th
eybe
gin
bylis
ting
itfo
ra
pric
eth
atis
gre
ater
than
wha
tth
eyex
pect
tore
ceiv
e.T
helo
nger
aho
me
ison
the
mar
ket,
wit
hout
bein
gso
ld,
the
mor
eth
epr
ice
drop
s.A
real
tor
sele
cts
50ho
mes
that
are
curr
entl
yli
sted
for
sale
.A
scat
terp
lot
reve
als
that
the
asso
ciat
ion
betw
een
x=
the
num
ber
ofda
ysth
eho
me
ison
the
mar
ket
andy
the
curr
ent
aski
ngpr
ice
($)
isfa
irly
linea
ran
dca
nbe
mod
eled
byth
eeq
uati
on
=24
5,00
0—
200x
.A
ddit
iona
lly,
85.4
%of
the
vari
atio
nin
the
curr
ent
aski
ngpr
ice
can
be
expl
aine
dby
this
line
arm
odel
.W
hich
ofth
efo
llow
ing
isth
eva
lue
ofth
eco
rrel
atio
n(r)
for
the
rela
tion
ship
betw
een
xan
dy?
(A)
-200
(B)
-0.9
24
(C)
0.14
6
(D)
0.85
4
(E)
0.92
4
6.A
ctiv
eis
anen
ergy
drin
kth
atcl
aim
sto
prov
ide
phys
ical
stre
ngth
.T
ote
stth
iscl
aim
,th
e
prod
ucer
sof
Act
ive
cond
ucte
da
stud
y.T
heco
mpa
nyre
crui
ted
25hi
ghsc
hool
athl
etes
and
4
prof
essi
onal
foot
ball
play
ers
topa
rtic
ipat
ein
the
stud
y.T
hehi
ghsc
hool
athl
etes
wer
eea
ch
rand
omly
assi
gned
todr
ink
betw
een
1an
d5
ounc
esof
Act
ive.
The
prof
essi
onal
foot
ball
play
ers
wer
eas
sign
edto
drin
kei
ther
30or
31ou
nces
.A
fter
wai
ting
10m
inut
esth
ey
com
plet
edas
man
ypu
ll-u
psas
they
coul
d.H
ere
isa
scat
terp
lot
show
ing
the
num
ber
of
ener
gydr
inks
cons
umed
and
the
num
ber
ofpu
llup
sth
atw
ere
com
plet
edby
each
part
icip
ant,
asw
ell
asa
line
ofbe
stfit
.
Whi
chof
the
foll
owin
gw
ould
incr
ease
if
the
prof
essi
onal
foot
ball
play
ers
wer
e
rem
oved
from
the
data
set?
(A)
(C)
the
slop
e
(D)
the
stan
dard
devi
atio
nof
the
resi
dual
s
(E)
Non
eof
the
abov
e.
L
•D
idno
tdi
e
Din
d
(B)
r2
:0 33 25 13
C z
+ST
ATS
MED
IC
.
1015
1025
Ntt
mb*
liD
Our
tCfl
cC
or,u
ryte
d
30i
4.ST
ATS
MED
IC
..
0...
7.C
erta
inca
rm
anuf
actu
rers
inst
all
aga
uge
that
tells
the
driv
erho
wm
any
mile
sth
eyca
ndr
ive
until
they
will
run
Out
of
gas.
Ast
udy
was
conduct
edto
test
the
accu
racy
ofth
ese
gaug
es.
Eac
hdr
iver
was
assi
gned
ace
rtai
nga
uge
read
ing
until
empt
yto
wat
chfo
r.W
hen
thei
rca
ran
noun
ced
itha
dth
atm
any
mile
sre
mai
ning
until
empt
y,th
eybe
gan
tom
easu
reth
eir
dist
ance
trav
eled
.A
fter
they
ran
out
ofga
s,th
eyre
port
edth
edi
stan
ceth
eyw
ere
able
todr
ive
(inm
iles)
asw
ell
asth
egau
ge
read
ing
they
wer
eas
sign
ed(in
mile
s).
Her
eis
com
pute
rou
tput
show
ing
the
regr
essi
onan
alys
is:
Reg
ress
ion
Ana
lysi
s:D
ista
nce
vers
usG
auge
Rea
ding
Pre
dict
orC
oef
SEC
oef
T
Con
stan
t—
0.79
283.
2114
Gau
ge1.
1889
0.04
57
s=
7.00
32R
-Sq
=0.
9326
Iden
tify
and
inte
rpre
tth
esl
ope
ofth
ere
gres
sion
line
used
for
pred
icti
ngth
eac
tual
dist
ance
that
can
bedr
iven
base
don
the
gaug
ere
adin
g.
(A)
Slop
e=
1.18
89.
The
pred
icte
ddi
stan
ceth
edr
iver
sw
ere
able
todr
ive
incr
ease
sby
1.18
89m
iles
for
each
addi
tion
alm
ilere
port
edby
the
gaug
e.(B
)S
lope
=0.
0457
.T
hepr
edic
ted
dist
ance
the
driv
ers
wer
eab
leto
driv
ein
crea
ses
by0.
0457
mile
sfo
rea
chad
diti
onal
mile
repo
rted
byth
ega
uge.
(C)
Slo
pe=
—0.
7928
.T
hepr
edic
ted
dist
ance
the
driv
ers
wer
eab
leto
driv
ed
ecre
ases
by0.
7928
mile
sfo
rea
chad
diti
onal
mile
repo
rted
byth
ega
uge.
(D)
Slo
pe=
1.18
89.
For
each
addi
tion
alm
ilere
port
edby
the
gaug
e,th
edr
iver
sw
ere
able
todr
ive
anad
diti
onal
1.18
89m
iles.
(E)
Slo
pe=
0.04
57.
For
each
addi
tion
alm
ilere
port
edby
the
gaug
e,th
edr
iver
sw
ere
able
todr
ive
anad
diti
onal
0.04
57m
iles.
8.A
wel
l-ba
lanc
edst
ock
mar
ket
port
folio
will
oft
enex
peri
ence
anex
pone
ntia
lgr
owth
.A
part
icul
arin
vest
orw
itha
wel
l-ba
lanc
edst
ock
mar
ket
port
foli
ore
cord
sth
epo
rtfo
lio
bala
nce
ever
ym
onth
,in
thou
sand
sof
doll
ars,
from
the
dat
eof
inve
stm
ent.
The
roug
hly
expo
nent
ial
grow
thca
nbe
tran
sfor
med
toa
line
arm
odel
bypl
otti
ngth
ena
tura
llo
gof
the
bala
nces
vers
usti
me,
inm
onth
s,w
here
t=
0re
pres
ents
the
date
the
mon
eyw
asin
vest
ed.
The
linea
rre
gres
sion
equa
tion
for
the
tran
sfor
med
data
is
In(b
alan
ce)=
5.55
0+
0.05
2t.
Usi
ngth
iseq
uati
on,
wha
tis
the
pred
icte
dba
lanc
eof
the
port
foli
oaf
ter
2ye
ars
(24
mon
ths)
?
(A)
$5,6
54
(B)
$6,7
98
(C)
$285
431
(D)
S89
6053
(E)
$948
,464
9.A
tC
entr
alH
igh
Sch
ool,
28%
ofth
est
uden
tsar
eF
resh
men
,26
%ar
eS
opho
mor
es,
24%
are
Juni
ors,
and
22%
are
Sen
iors
.T
hest
ud
ent
man
ager
ofth
esc
hool
new
spap
erw
ould
like
toco
nduc
ta
surv
eyto
esti
mat
eth
epr
opor
tion
ofea
chcl
ass
that
plan
sto
atte
nd
the
upco
min
gF
ootb
all
gam
e.S
hesu
gges
tssu
rvey
ing
ara
ndom
sam
ple
of10
0st
uden
ts,
but
spec
ific
ally
byse
lect
ing
rand
omsa
mpl
esof
28F
resh
men
,26
Sop
hom
ores
,24
Juni
ors,
and
22S
enio
rs.
Whi
chof
the
foll
owin
gis
atr
uest
atem
ent
abo
ut
this
sam
plin
gpr
oced
ure?
(A)
Thi
sis
asi
mpl
era
ndom
sam
ple
beca
use
stud
ents
ofev
ery
clas
sha
vean
equa
lch
ance
of
bein
gse
lect
ed.
(B)
Thi
sis
acl
uste
rra
ndom
sam
ple
beca
use
ther
ear
e4
grou
psof
stud
ents
that
are
tobe
sele
cted
.
(C)
Thi
sis
aco
nven
ienc
esa
mpl
ebe
caus
eon
ly10
0st
uden
tsar
esu
rvey
ed,
whi
chis
am
anag
eabl
esi
ze.
(D)
Thi
sis
ast
rati
fied
rand
omsa
mpl
ebe
caus
ea
sep
arat
era
ndom
sam
ple
isse
lect
edfr
om
each
clas
s.
(E)
Thi
sis
asy
stem
atic
rand
omsa
mpl
ebe
caus
eea
chcl
ass
mak
esup
appr
oxim
atel
yon
e-
four
thof
the
stu
den
tbo
dy.
P 0.80
60
0.00
00
—0.
2469
26.0
310
R-S
q(ad
j)=
0.93
12
+ST
ATS
MED
IC+
STAT
SM
EDIC
10.A
stud
yis
cond
ucte
dto
inve
stig
ate
whe
ther
cust
omer
sati
sfac
tion
isg
reat
eram
ong
com
pute
r
com
pani
esth
atof
fer
tech
supp
ort
vers
usth
ose
that
dono
tof
fer
tech
supp
ort.
Ara
ndom
sam
ple
of50
cust
omer
sar
ese
lect
edfr
omam
ong
thos
eth
atpu
rcha
sed
com
pute
rsth
atof
fer
tech
supp
ort.
Ase
par
ate
rand
omsa
mpl
eof
40cu
stom
ers
are
sele
cted
from
amon
gth
ose
that
purc
hase
dco
mpu
ters
that
dono
tof
fer
tech
supp
ort.
The
stud
yfo
und
that
the
mea
nsa
tisf
acti
onra
ting
was
sign
ific
antly
grea
ter
amon
gcu
stom
ers
that
purc
hase
dco
mpu
ters
that
offe
rte
chsu
ppor
t.
Whi
chof
the
follo
win
gis
the
best
desc
ript
ion
ofth
isst
udy?
(A)
An
expe
rim
ent
usin
ga
com
plet
ely
rand
omiz
edde
sign
.
(B)
An
expe
rim
ent
usin
ga
rand
omiz
edbl
ock
desi
gn.
(C)
An
expe
rim
ent
usin
ga
mat
ched
pair
sde
sign
.
(D)
An
obse
rvat
iona
lst
udy
usin
ga
sim
ple
rand
omsa
mpl
e.
(E)
An
obse
rvat
iona
lst
udy
usin
ga
stra
tifi
edsa
mpl
e.
11T
oddl
ers
tend
toha
vean
abun
danc
eof
ener
gy.
To
put
that
ener
gyto
go
od
use
afi
tnes
s
inst
ruct
orcr
eate
sa
Tod
dler
Fit
ness
clas
s,In
this
clas
sth
epa
rtic
ipan
tsha
veto
doev
eryt
hing
the
fitn
ess
inst
ruct
or’s
ener
geti
cto
ddle
rd
aug
hte
rdo
es.
To
com
pare
the
num
ber
ofca
lori
esbu
rned
inT
oddl
erF
itne
ssve
rsus
the
stan
dard
fitn
ess
clas
s
40vo
lunt
eers
are
recr
uite
d.T
hevo
lunt
eers
are
assi
gned
atra
ndom
topa
rtic
ipat
ein
Tod
dler
Fit
ness
orth
est
anda
rdfi
tnes
scl
ass.
Eac
hpa
rtic
ipan
tw
ears
aca
lori
eco
unti
ngfi
tnes
sw
atch
.
At
the
end
ofth
ecl
ass
the
calo
ries
burn
edby
each
part
icip
ant
isre
cord
edan
dth
eav
erag
e
num
ber
ofca
lori
esbu
rned
isca
lcul
ated
for
each
clas
s.
Aft
erth
ecl
asse
sen
ded
,th
ein
stru
ctor
lear
ned
that
the
mea
nnu
mbe
rof
calo
ries
burn
edby
the
part
icip
ants
inT
oddl
erF
itne
ssw
assi
gnif
ican
tlygr
eate
rth
anth
em
ean
num
ber
ofca
lori
es
burn
edby
the
part
icip
ants
inth
est
anda
rdfi
tnes
scl
ass.
Whi
chof
the
foll
owin
gis
the
mos
tap
prop
riat
eco
nclu
sion
?
(A)
The
reis
conv
inci
ngev
iden
ceth
atT
oddl
erF
itne
ssca
used
the
part
icip
ants
tobu
rnm
ore
calo
ries
than
the
stan
dard
fitn
ess
clas
s,an
dth
eco
nclu
sion
can
bege
nera
lize
dto
all
adul
ts
that
wor
kout
.
(B)
The
reis
conv
inci
ngev
iden
ceth
atT
oddl
erF
itne
ssca
used
the
part
icip
ants
tobu
rnm
ore
calo
ries
than
the
stan
dard
fitn
ess
clas
s,an
dth
eco
nclu
sion
can
bege
nera
lize
dto
all
stud
ents
ofth
isfi
tnes
sin
stru
ctor
,
(C)
The
reis
conv
inci
ngev
iden
ceth
atT
oddl
erF
itne
ssca
used
the
part
icip
ants
tobu
rnm
ore
calo
ries
than
the
stan
dard
fitn
ess
clas
s,an
dth
eco
nclu
sion
cann
otbe
gene
rali
zed
beyo
nd
thos
ein
the
stud
y.
(D)
Cau
se-a
nd-e
ffec
tca
nnot
bees
tabl
ishe
d,bu
tth
ere
isan
asso
ciat
ion
betw
een
the
type
of
exer
cise
clas
sta
ken
and
the
num
ber
ofca
lori
esbu
rned
inth
epo
pula
tion
ofal
lad
ults
that
wor
kout
.
(E)
Cau
se-a
nd-e
ffec
tca
nnot
bees
tabl
ishe
d,bu
tth
ere
isan
asso
ciat
ion
betw
een
the
type
of
exer
cise
clas
sta
ken
and
the
num
ber
ofca
lori
esbu
rned
inth
epo
pula
tion
ofal
lst
uden
tsof
this
fitn
ess
inst
ruct
or.
+ST
ATS
MED
IC
..
‘4”ST
ATS
MED
IC
.
...........,..
.
12.I
nor
der
toes
timat
eth
epr
opor
tion
ofst
uden
tsth
atte
xtw
hile
driv
ing,
asc
hool
adm
inis
trat
orse
lect
sa
sim
ple
rand
omsa
mpl
eof
stud
ents
from
alis
tof
all
stud
ents
atth
esc
hool
who
have
park
ing
perm
its.
The
stud
ents
are
call
edto
the
offi
ce,
one
ata
tim
e.T
head
min
istr
ator
asks
each
stud
ent,
“Do
you
text
whi
ledr
ivin
g,ev
enth
ough
you
are
not
supp
osed
to?”
Bas
edon
the
surv
ey,
the
adm
inis
trat
ores
tim
ates
that
only
2%of
stud
ents
with
park
ing
pass
este
xtw
hile
driv
ing.
Wha
tpo
tent
ial
bias
ispr
esen
tin
the
desi
gnof
this
surv
eyan
dw
hat
isth
elik
ely
dire
ctio
nof
the
bias
?
(A)
The
sam
ple
prop
orti
onis
likel
yan
unde
rest
imat
eof
the
popu
lati
onpr
opor
tion
due
tore
spon
sebi
as.
(B)
The
sam
ple
prop
orti
onis
likel
yan
unde
rest
imat
eof
the
popu
lati
onpr
opor
tion
due
toun
derc
over
age.
(C)
The
sam
ple
prop
orti
onis
likel
yan
unde
rest
imat
eof
the
popu
lati
onpr
opor
tion
due
tono
nres
pons
e.
(D)T
hesa
mpl
epr
opor
tion
islik
ely
anov
eres
tim
ate
ofth
epo
pula
tion
prop
orti
ondu
eto
resp
onse
bias
.
(E)
The
sam
ple
prop
orti
onis
likel
yan
over
esti
mat
eof
the
popu
lati
onpr
opor
tion
due
toun
derc
over
age.
13.T
hegu
idan
ceco
unse
lor
ofa
larg
ehi
ghsc
hool
repo
rts
that
48.5
%of
Juni
orPr
e-C
alcu
lus
stud
ents
sign
edup
tota
keA
PSt
atis
tics
next
year
,52
.5%
sign
edup
tota
keA
PC
alcu
lus
next
year
and
10%
ofJu
nior
Pre-
Cal
culu
sst
uden
tssi
gned
upto
take
both
AP
Stat
istic
san
dA
PC
alcu
lus
next
year
.If
one
Juni
orPr
e-C
alcu
lus
stud
ent
isse
lect
edat
rand
om,
wha
tis
the
prob
abil
ity
that
they
did
not
sign
upto
take
AP
Stat
istic
sor
AP
Cal
culu
sne
xtye
ar?
(A)
0.09
(B)0
.11
(C)0
.19
(D)
0.91
(F)
Not
enou
ghin
form
atio
nis
give
nto
dete
rmin
eth
epr
obab
ility
.
14.A
non
line
clot
hing
com
pany
deci
des
toin
vest
igat
ew
heth
erof
feri
ngth
eir
cust
omer
sa
coup
onup
onco
mpl
etio
nof
thei
rfi
rst
purc
hase
will
enco
urag
eth
emto
mak
ea
seco
ndpu
rcha
se.
To
doso
,th
eco
mpa
nypr
ogra
ms
the
web
site
tora
ndom
lyse
lect
100
firs
ttim
ecu
stom
ers.
Sixt
y
ofth
ese
cust
omer
sar
era
ndom
lyse
lect
edto
rece
ive
aco
upon
for
$5of
fth
eir
next
purc
hase
,
tobe
mad
ein
the
next
30da
ys.
The
othe
r40
cust
omer
sar
eno
tof
fere
da
coup
on.
The
tabl
ebe
low
show
sth
enu
mbe
rof
cust
omer
sin
each
grou
pth
atm
ade
ase
cond
purc
hase
with
in30
days
ofth
eir
firs
tpu
rcha
se.
Sent
aco
upon
afte
rth
efi
rst
purc
hase
?
[:1IIIIIIII1
..
ta
Mad
ea
seco
ndIF
1:34
1650
purc
has
:wh
n
Iiir1
2624
50
ITot
a160
4010
0
Bas
edup
onth
eta
ble,
is“y
es,
mad
ea
seco
ndpu
rcha
se”
inde
pend
ent
of“y
es,
bein
gse
nta
coup
on”?
(A)
Yes
,ex
actly
half
ofth
ecu
stom
ers
mad
ea
seco
ndpu
rcha
sean
dha
lfdi
dno
t.
(B)
Yes
,th
ela
rges
tco
unt
inth
eta
ble
com
esfr
omth
ose
who
wer
ese
nta
coup
onan
dm
ade
ase
cond
purc
hase
with
in30
days
.
(C)
No,
the
prob
abil
ity
ofm
akin
ga
seco
ndpu
rcha
seis
not
equa
lto
the
prob
abil
ity
ofm
akin
g
ase
cond
purc
hase
give
nth
ata
coup
onw
asse
nt.
(D)
No,
the
prob
abil
ity
ofm
akin
ga
seco
ndpu
rcha
seis
the
sam
ew
heth
eror
not
aco
upon
was
sent
.
(E)
Itis
impo
ssib
leto
draw
aco
nclu
sion
abou
tin
depe
nden
cebe
caus
ea
coup
onw
asno
tse
nt
toex
actly
half
ofth
ecu
stom
ers.
15.A
sth
esa
ying
goes
,“Y
ouca
n’t
plea
seev
eryo
ne.”
Stu
dies
have
show
nth
atin
ala
rge
popu
lati
onap
prox
imat
ely
4.5%
ofth
epo
pula
tion
will
bedi
sple
ased
,re
gard
less
ofth
e
situ
atio
n.If
ara
ndom
sam
ple
of25
peop
lear
ese
lect
edfr
omsu
cha
popu
lati
on,
wha
tis
the
prob
abil
ity
that
atle
ast
two
will
bedi
sple
ased
?
(A)
0.04
5(B
)0.
311
(C)
0.37
3
(D)
0.62
7
(F)
0.68
8
+ST
ATS
MED
IC+
STAT
SM
EDIC
16. M
any
urba
nzo
osar
elo
okin
gat
way
sto
effe
ctiv
ely
hand
lean
imal
was
te.
One
zoo
has
inst
alle
d
afa
cilit
yth
atw
illtr
ansf
orm
anim
alw
aste
into
elec
tric
ity.
To
esti
mat
eho
wm
any
poun
dsof
was
teth
eym
ayha
veto
fuel
the
new
faci
lity
they
bega
nke
epin
gm
etic
ulou
sre
cord
s.T
hey
disc
over
edth
atth
eam
ount
ofan
imal
was
teth
eyw
ere
disp
osin
gof
daily
isap
prox
imat
ely
Nor
mal
with
am
ean
of34
8.5
poun
dsan
da
stan
dard
devi
atio
nof
38.2
poun
ds.
Am
ount
sov
er
350
poun
dsw
ould
gen
erat
een
ough
elec
tric
ity
toco
ver
wha
tis
nee
ded
tofo
rth
een
tire
aqua
rium
that
day.
App
roxi
mat
ely
wha
tpr
opor
tion
ofth
eda
ysca
nth
ezo
oex
pect
toob
tain
enou
ghw
aste
toco
ver
wha
tis
nee
ded
toru
nth
een
tire
aqua
rium
for
the
day?
(A)
0.48
4
(B)
0.49
9
(C)
0.51
6
(D)0
.680
(E)
0.95
0
17.S
tude
nts
ina
stat
isti
cscl
ass
part
icip
ated
ina
proj
ect
inw
hich
they
atte
mpte
dto
esti
mat
eth
e
true
mea
nhe
ight
ofal
lst
uden
tsin
thei
rla
rge
high
scho
ol.
The
stud
ents
wer
esp
lit
into
4
grou
ps.
Eac
hgr
oup
had
thei
row
nsa
mpl
ing
met
hod,
and
they
used
itto
sele
cta
sam
ple
each
day
for
50da
ys.
Bel
owar
eth
ees
tim
ates
base
don
thei
r50
sam
ples
:
14 12 12
,,
Is
51
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ICs
=2)
5560
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h)
Aft
erth
esa
mpl
esw
ere
coll
ecte
dan
dth
em
eans
wer
epl
otte
dth
ete
ach
ervi
site
dth
esc
hool
nurs
ew
hoto
ldhe
rth
atth
etr
uem
ean
heig
htof
all
stud
ents
inth
esc
hool
is67
.5in
ches
.
Whi
chgr
oup
prod
uced
sam
ple
stat
isti
csth
ates
tim
ated
the
true
valu
eof
the
para
met
erw
ith
rela
tivel
ylo
wbi
asan
dlo
wva
riab
ility
?
(A)
Gro
up1
(8)
Gro
up2
(C)
Gro
up3
(D)
Gro
up4
(E)
All
grou
pspr
oduc
edst
atis
tics
that
have
low
bias
and
low
vari
abili
tybe
caus
et
isan
unbi
ased
esti
mat
orof
i.
5’
10
to
54 14 10 0 II 12 10 ‘3 14
Oo
p2(s
=1
01
DO6’
)65
1075
80
4’ST
ATS
MED
IC
..
4’ST
ATS
MED
IC
.
.18
.Eve
ryye
arat
the
AP
Stat
istic
sEx
amre
adin
gap
pare
lis
sold
toco
mm
emor
ate
the
even
t.B
ased
onhi
stor
ical
data
,w
ekn
owth
at56
%of
teac
hers
will
mak
ean
appa
rel
purc
hase
.T
his
year
,th
eor
gani
zers
have
deci
ded
tose
lect
ara
ndom
sam
ple
of50
teac
hers
.If
ase
lect
edte
ache
rm
ade
anap
pare
lpu
rcha
se,
they
will
begi
ven
apr
ize.
Wha
tis
the
prob
abil
ity
that
mor
eth
an60
%of
the
sele
cted
teac
hers
will
win
apr
ize?
(A)
App
roxi
mat
ely
0(B
)0.
007
(C)
0.28
4
(D)
0.46
8(E
)0.
600
19.A
car
deal
ersh
iplo
oks
back
atth
eir
prev
ious
year
’ssa
les
reco
rds.
Las
t yea
r,th
ede
aler
ship
sold
422
vehi
cles
.T
hem
ean
sale
spr
ice
was
$24,
500
with
ast
anda
rdde
viat
ion
of$1
2,87
5.T
hede
aler
ship
also
disc
over
edth
atth
edi
stri
buti
onof
the
sale
spr
ices
issk
ewed
toth
eri
ght.
Ifth
ede
aler
ship
wer
eto
sele
ctre
peat
edra
ndom
sam
ples
of40
vehi
cles
from
the
popu
lati
onof
all
vehi
cles
sold
last
year
and
calc
ulat
eth
eav
erag
esa
lepr
ice
for
each
sam
ple
of40
,w
hich
ofth
efo
llow
ing
give
sth
eco
rrec
tm
ean
and
stan
dard
devi
atio
nof
the
sam
plin
gdi
stri
buti
onof
the
sam
ple
mea
n?
(A)
Mea
n=
$24,
500,
Sta
ndar
dde
viat
ion
=
(B)
Mea
n=
$24,
500,
Stan
dard
devi
atio
n=
40
(C)
Mea
n=,
Sta
ndar
dde
viat
ion
=12
,875
(D)
Mea
n=
Sta
ndar
dde
viat
ion
=12
,875
40(E
)C
anno
tbe
dete
rmin
edbe
caus
eth
esa
mpl
esi
zeis
smal
l.
.20
.The
spee
dof
pick
upof
ride
shar
ing
serv
ices
like
Ube
ran
dLy
ftse
ems
toha
vesu
rpas
sed
that
ofam
bula
nce
serv
ices
.T
hem
ean
resp
onse
tim
eof
ambu
lanc
esac
ross
the
Uni
ted
Sta
tes
is
15.3
min
utes
with
ast
anda
rdde
viat
ion
of12
.8m
inut
es.
For
ride
shar
ing
serv
ices
,th
em
ean
pick
-up
tim
eac
ross
the
Uni
ted
Sta
tes
is8
min
utes
with
ast
anda
rdde
viat
ion
of5.
2m
inut
es.
Bas
edon
thes
ees
tim
ates
,w
hich
ofth
efo
llow
ing
give
sth
est
anda
rdde
viat
ion
ofth
esa
mpl
ing
dist
ribu
tion
ofth
edi
ffer
ence
inth
esa
mpl
em
eans
for
sam
ples
of30
ambu
lanc
eri
des
and
40ri
desh
arin
gri
des
(Am
bula
nce
—R
ide
Sha
ring
)?
12.8
5.2
(A) B
128
5.2
(C
)+
(D)Ii_
__2—
V30
40(E
)C
anno
tbe
dete
rmin
edbe
caus
eth
eco
ndit
ions
are
not
met
.
21.A
poll
was
cond
ucte
dus
ing
asa
mpl
eof
2500
regi
ster
edvo
ters
tode
term
ine
wha
tpr
opor
tion
ofvo
ters
are
plan
ning
tovo
tefo
rth
ein
cum
bent
pres
iden
tin
the
upco
min
gel
ecti
on.
The
poll
ster
sre
port
ed,
“We
are
95%
conf
iden
tth
atth
etr
uepr
opor
tion
ofre
gist
ered
vote
rsth
at
will
vote
for
the
incu
mbe
ntpr
esid
ent
isw
ithin
the
inte
rval
0.46
5to
0.54
5.”
Wha
tis
mea
ntby
95%
conf
iden
ce?
(A)
The
poll
ster
sus
eda
met
hod
that
isg
uar
ante
edto
capt
ure
the
true
voti
ngpr
efer
ence
of
95%
ofth
ere
gist
ered
vote
rs.
(B)
The
poll
ster
sus
eda
met
hod
that
will
capt
ure
the
true
popu
lati
onpr
opor
tion
inab
out
95%
ofal
lpo
ssib
leco
nfid
ence
inte
rval
sb
ased
upon
rand
omsa
mpl
esof
size
2500
from
this
popu
lati
on.
(C)
The
poll
ster
sca
nbe
95%
conf
iden
tth
atth
ein
cum
bent
pres
iden
tw
illre
ceiv
e50
.5%
ofth
e
vote
and
will
win
the
elec
tion
.
(D)
The
reis
a95
%ch
ance
that
the
inte
rval
(0.4
65,
0.54
5)co
ntai
nsth
etr
uepr
opor
tion
of
vote
rsth
atar
epl
anni
ngto
vote
for
the
incu
mbe
ntpr
esid
ent.
(E)
Ifth
epo
llst
ers
take
man
yra
ndom
sam
ples
ofsi
ze25
00fr
omth
ispo
pula
tion
,ab
ou
t95
%of
the
resu
ltin
gin
terv
als
will
cont
ain
0.50
5.
+ST
ATS
MED
IC+
STAT
SM
EDIC
0
>‘Coci
Co
E
o
D
a)
a)Ec
w
+ .
>,a)
U,
a) ci
U,
0-
a)0)0 COCO
U,_o0-
a)U,U,
w
+
IC
‘cC
-H
‘0C
U
.
25.A
stud
ent
wou
ldlik
eto
esti
mat
eth
epr
opor
tion
ofth
ese
nior
clas
sth
atpl
ans
toat
tend
prom
this
year
.T
hest
uden
tgo
esto
the
guid
ance
offi
cean
dge
tsa
listo
fth
ena
mes
ofal
l27
4se
nior
s.U
sing
the
list,
she
sele
cts
asi
mpl
era
ndom
sam
ple
of50
stud
ents
and
find
sth
at76
%of
the
sele
cted
stud
ents
plan
toat
tend
prom
this
year
.Sh
ew
ould
like
toco
nstr
uct
a95
%co
nfid
ence
inte
rval
for
the
prop
orti
onof
the
enti
rese
nior
clas
sth
atpl
ans
toat
tend
prom
this
year
.A
reth
eco
ndit
ions
for
infe
renc
em
et?
(A)
Yes
,al
lco
ndit
ions
for
infe
renc
ear
em
et.
(B)
No,
alth
ough
the
rand
oman
dla
rge
coun
tsco
ndit
ions
are
met
,th
e10
%co
ndit
ion
isno
tm
et.
(C)
No,
alth
ough
the
rand
oman
d10
%co
ndit
ions
are
met
,th
ela
rge
coun
tsco
ndit
ion
isno
tm
et.
(D)
No,
ther
ear
etw
oco
ndit
ions
for
infe
renc
eth
atar
eno
tm
et.
(E)
No,
none
ofth
eco
ndit
ions
for
infe
renc
ear
em
et.
26.L
exie
isa
wai
tres
s.Sh
ebe
liev
esth
atsh
eea
rns
mor
etip
s,on
aver
age,
whe
nsh
ecu
rls
her
hair
befo
rew
ork
rath
erth
anpu
lling
itba
ckin
apo
nyta
il.In
orde
rto
inve
stig
ate
this
belie
f,sh
ew
rite
s“c
urls
”on
30sl
ips
ofpa
per
and
“pon
ytai
l”on
30sl
ips
ofpa
per,
puts
them
ina
hat
and
mix
esth
emw
ell.
Eac
hti
me
she
gets
read
yfo
rw
ork
she
rand
omly
sele
cts
one
piec
eof
pape
rto
dete
rmin
eho
wsh
esh
ould
dohe
rha
irth
atda
y.U
sing
the
data
she
colle
cts,
she
carr
ies
out
atte
stfo
ra
diff
eren
cein
mea
nsin
orde
rto
test
thes
ehy
poth
eses
:
Ho:
Pc=
pp
H:
jic
>pp
Whe
re/l
c=
the
mea
nam
ount
oftip
sth
atL
exie
wou
ldm
ake
for
all
days
inw
hich
she
curl
she
rha
iran
dpp
=th
em
ean
amou
ntof
tips
that
Lex
iew
ould
mak
efo
ral
lda
ysin
whi
chsh
epu
llshe
rha
irup
ina
pony
tail.
The
P-va
lue
ofth
iste
stis
0.03
75.
Wha
tis
the
inte
rpre
tati
onof
this
valu
e?
(A)
Ass
umin
gth
etr
uedi
ffer
ence
(Cur
ls—
Pony
tail)
inth
em
ean
amou
ntof
tips
rece
ived
is0,
ther
eis
a0.
0375
prob
abil
ity
that
Lexi
ew
ould
obse
rve
adi
ffer
ence
insa
mpl
em
eans
asgr
eate
ror
grea
ter
than
she
did
bych
ance
alon
e.(B
)A
ssum
ing
that
the
true
mea
nam
ount
ofti
psth
atLe
xie
wou
ldre
ceiv
ew
hile
wea
ring
curl
sis
grea
ter
than
the
true
mea
nam
ount
ofti
psth
atL
exie
wou
ldre
ceiv
ew
hile
wea
ring
her
hair
ina
pony
tail,
ther
eis
0.03
75pr
obab
ilit
yth
atth
enu
llhy
poth
esis
wou
ldbe
reje
cted
.
(C)
The
P-va
lue
indi
cate
sth
atth
ere
isa
prob
abil
ity
of0.
0375
that
the
null
hypo
thes
isis
true
.(D
)B
ecau
seth
eP-
valu
eis
less
than
a=
0.05
,L
exie
shou
ldfa
ilto
reje
ctth
enu
llhy
poth
esis
and
inte
rpre
tth
ere
sults
tom
ean
that
she
has
prov
enth
atsh
em
akes
mor
em
oney
intip
sw
hen
she
curl
she
rha
ir.
(E)
The
reis
a0.
0375
prob
abil
ity
that
Lex
iew
illm
ake
mor
em
oney
inti
psw
hen
she
wea
rshe
rha
irin
curl
sop
pose
dto
wea
ring
her
hair
ina
pony
tail.
27.J
osh
wan
tsto
conv
ince
his
mot
her
tost
opbu
ying
sing
le-p
lyto
ilet
pape
r.Jo
shbe
liev
esth
atev
enth
ough
Fluf
fy,
atw
o-pl
yto
ilet
pape
rco
sts
mor
e,it
will
last
long
erbe
caus
eit
ism
ore
abso
rben
t.T
ohe
lpsu
bsta
ntia
tehi
scl
aim
,Jo
shpe
rfor
med
ast
udy.
He
purc
hase
da
rand
omsa
mpl
eof
18ro
llsof
Fluf
fy.
For
each
roll,
hede
term
ined
how
man
ysq
uare
sar
ene
eded
toco
mpl
etel
yab
sorb
one-
quar
ter
cup
ofw
ater
.H
ere
isa
dotp
lot
ofth
eda
ta.
Num
ber
ofS
quar
es
The
mea
nof
the
sam
ple
is24
.444
squa
res
with
ast
anda
rdde
viat
ion
of2.
45sq
uare
s.Si
ngle
-pl
yto
ilet
pape
rre
quir
es26
squa
res
toab
sorb
one-
quar
ter
cup
ofw
ater
.Jo
shw
ould
like
toca
rry
Out
ate
stto
dete
rmin
eif
ther
eis
conv
inci
ngev
iden
ceth
atth
em
ean
num
ber
ofsq
uare
sof
Fluf
fyth
atar
ene
eded
toab
sorb
one-
quar
ter
cup
ofw
ater
isfe
wer
than
26sq
uare
s.W
hat
isth
eap
prop
riat
ete
stst
atis
tican
dP-
valu
eof
this
test
?
(A)
z=
—2.
69,
P-va
lue
=0.
0036
(B)
t=
—2.
69,
P-va
lue
=0.
0078
(C)
t=
—2.
69,
P-va
lue
=0.
0156
(D)
t=
2.69
,P-
valu
e=
0.99
22
(E)
z=
2.69
,P-
valu
e0.
9964
B 2021
08
2627
BB
2529
‘4’ST
ATS
MED
IC+
STAT
SM
EDIC
28.E
rica
has
asw
imm
ing
pooi
athe
rho
use.
Onc
ea
year
she
purc
hase
sa
50-p
ound
buck
etof
chlo
rine
pell
ets
from
anon
line
com
pany
.O
utof
curi
osit
ysh
ew
eigh
sth
ebu
cket
and
find
sth
at
iton
lyw
eigh
s46
.2po
unds
.S
hepu
rcha
ses
4m
ore
50-p
ound
buck
ets,
givi
nghe
ran
SRS
of
size
5.T
hem
ean
wei
ght
ofth
e5
buck
ets
is48
.5po
unds
.S
hesu
spec
tsth
atth
eco
mpa
nyis
chea
ting
the
cust
omer
s.S
heus
eshe
rda
tato
test
the
hypo
thes
esHo
:p
=50
poun
dsve
rsus
H:
p<
50po
unds
.T
heP-
valu
eof
her
test
is0.
0851
.W
hat
deci
sion
shou
ldsh
em
ake
and
wha
tty
peof
erro
rco
uld
she
mak
eas
are
sult
ofhe
rde
cisi
on?
(A)
She
shou
ldre
ject
Ho.
She
coul
dm
ake
aT
ype
Ierr
or,
mea
ning
she
find
sco
nvin
cing
evid
ence
that
the
true
mea
nw
eigh
tof
the
50-p
ound
buck
ets
isle
ssth
an50
poun
dsw
hen
inre
ality
itis
not.
(B)
She
shou
ldre
ject
Ho.
She
coul
dm
ake
aT
ype
IIer
ror,
mea
ning
she
fails
tofi
ndco
nvin
cing
evid
ence
that
the
true
mea
nw
eigh
tof
the
50-p
ound
buck
ets
isle
ssth
an50
poun
dsw
hen
inre
ality
itis.
(C)
She
shou
ldfa
ilto
reje
ctH
o.S
heco
uld
mak
ea
Typ
eIe
rror
,m
eani
ngsh
efi
nds
conv
inci
ng
evid
ence
that
the
true
mea
nw
eigh
tof
the
50-p
ound
buck
ets
isle
ssth
an50
poun
dsw
hen
inre
ality
itis
not.
(D)
She
shou
ldfa
ilto
reje
ctH
oS
heco
uld
mak
ea
Typ
eII
erro
r,m
eani
ngsh
efa
ilsto
find
conv
inci
ngev
iden
ceth
atth
etr
uem
ean
wei
ght
ofth
e50
-pou
ndbu
cket
sis
less
than
50
poun
dsw
hen
inre
ality
itis.
(E)
She
shou
ldfa
ilto
reje
ctH
o.S
heco
uld
mak
ea
low
pow
erer
ror,
mea
ning
that
she
reje
cts
the
null
hypo
thes
isw
hen
the
null
hypo
thes
isis
true
.
29.A
psyc
holo
gica
lst
udy
foun
dth
atm
enw
how
ere
dist
ance
runn
ers
lived
,on
aver
age,
five
year
s
long
erth
anth
ose
who
wer
eno
tdi
stan
ceru
nner
s.T
hest
udy
was
cond
ucte
dus
ing
ara
ndom
sam
ple
of50
men
who
wer
edi
stan
ceru
nner
san
dan
ind
epen
den
tra
ndom
sam
ple
of30
men
who
wer
eno
tdi
stan
ceru
nner
s.T
hem
enw
how
ere
dist
ance
runn
ers
lived
tobe
84.2
year
s
old,
onav
erag
e,w
itha
stan
dard
devi
atio
nof
10.2
year
s.T
hem
enw
how
ere
not
dist
ance
runn
ers
lived
tobe
79.2
year
sol
d,on
aver
age,
with
ast
anda
rdde
viat
ion
of6.
8ye
ars.
Whi
chof
the
foll
owin
gis
the
test
stat
isti
cfo
rth
eap
prop
riat
ete
stto
dete
rmin
eif
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tVideo 1.1 Types of Displays
, S
E 11$
A B22
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7
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AP Exam Tips:
+ STATS MEDIC
Histogram: Find the median.
.Dotplot: Which distribution hasthe smallest standard deviation?
I I
U
Boxplot: Give 5-number summary and IQR Stemplot: Compare shapes
0 10 20 30 40 50 60
123456
fideo 1 .2 Describing a Distribution
SOCS + context
Shape Center Spread Outliers
Example: # hours of sleep
3 5 6 6 7 7 7 7 8 8
Describe the distribution.
.
AP Exam Tips:
+ STATS MEDIC
Video 2.1 Describing a Relationship
DUFS + context
Direction Unusual Features
Example: Heat bills
Describe the distribution
Interpret slope
Interpret r2 = 0.989
Form Strength
.
AP Exam Tips:
.+ STATS MEDIC
I
Equation J9 = 273.58 -_3.6x1
Average temperature (Fabtheit)
I I
a., [...:...i. .1. i.1 . .1.
1’. . ‘ ‘
‘ideo 2.2 Predictions
Example: Heat bills
and Residuals
-10
e
I I I
20 30 40 50 60 70Average temperature (PaIuenheft)
with an average temperature of 42° F.
AP Exam Tips:
log(heat bill)= 4.52— 1.57 log(average temp)
4. STATS MEDIC
0Equation
9=273.58-3.6x 5.
10-
0
.
Average temperature (Fahrenheit)
Find the predicted bill for a month with an average temperature of 42° F.
The actual bill for a month with average temperature of 42° F was $1 20. Calculate and interpret theresidual.
Is a linear model appropriate for the data set?
What if the data appears nonlinear? Use a nonlinear model to calculate a predicted bill for a month
___L____h__t___t___
Video 3.1 Sampling Methods and Issues
Sampling Methods:Picture: Convenience Sample
Voluntary Response Sample
Simple Random Sample
How to do an SRS
Sampling Issues:
Undercoverage
Nonresponse
Response Bias
Stratified vs. ClusterPicture: Stratified Cluster
AP Exam Tips:
‘I. STATS MEDIC
•ideo 3.2 Experimental Design
Average AP Exam Scores:Stats Medic 4.3Review book 3.8
Picture:
Confounding variable
Draw outline of the experiment:
•. .
What is the difference between an experiment and an observational study?
What is the advantage of an experiment over and observational study?
Block design
AP Exam Tips:
.
+ STATS MEDIC
Video 4.1 General Probability
R” “A N D”
Define mutually exclusive Define independent
No: No:
Yes: Yes
Example: Stella’s Lounge only sells burgers and sandwiches. Each comes with chips or, for $1 more,
it can be served with fries. The probability that a randomly selected customer orders a burger is
60%. If they order a burger, 70% of the time they will get fries. If the customer orders a sandwich,
they get fries 45% of the time. What is the probability that a randomly selected customer orders:
(a) A sandwich and fries
(b) Fries
(c) A sandwich, given they order fries
AP Exam Tips:
+ STATS MEDIC
®/ideo 4.2 Binomial Distributions
A certain NBA basketball player is an 85% free throw shooter, meaning he has an 85% probability of
making any given free throw. In one month he will shoot 100 free throws. Assume each shot isindependent of the others.
Let X = the number of free throws he makes out of 100 attempts.
(a) Describe the distribution of X.
(b) What is the probability that the basketball player makes exactly 80 free throws out of 100?
(c) Find the probability that the player makes at least 80 free throws out of 100.
AP Exam Tips:
‘I’ STATS MEDIC
Video 4.3 Transforming and Combining Random Variables
Transforming Random Variables
Numberhoursofsleep: 3 5 6 6 7 7 7 7 8 8
X- number of hours of sleep
Y — number of minutes of sleep = cr = =
Z — number of minutes of sleep= = =
(with 20 minute nap)
RULES: Mean SD Variance
Multiply/divide by A
Add/subtract B .Combining Random Variables
X - Number of hours of sleep for 1st hour. p=ó.4 =l.5l
Y - Number of hours of sleep for 2 hour. =6.2 = 1.98
S=X+Y D=X—Y
AP Exam Tips:
+ STATS MEDIC
Qideo 4.4 Normal Distribution Calculations
Example: The number of daily views at StatsMedic.com follows an approximately normal distribution
with a mean of 1 5,000 and a standard deviation of 4,000.
(a) Find the probability that a randomly selected day has more than 20,000 views.
(b) How many views would be in the bottom 5% of all days.
AP Exam Tips:
+ STATS MEDIC
Video 4.5 Geometric Distributions .Example: In 2016, the Bottle Flip Challenge (flipping a water bottle into the air and landing it right
side up) took the internet by storm. Michael is really good at the boffle flipping. On any given bottle
flip, he has a 35% probability of landing the bottle right side up. Assume that each bottle flip is
independent.
Let X = the number of flips it takes until Michael lands a bottle flip.
Conditions:
B:
F:
S:
(a) Describe the distribution of X.
(b) Find the probability that it takes Michael 4 flips until he lands the bottle right side up.
(c) Find the probability that Michael lands the bottle right side up within the first 4 flips.
AP Exam Tips:
+ STATS MEDIC
‘ideo 5.1 Introduction to Sampling Distributions
Picture A statistic estimates a parameter
Example: Find the average word length for Beyonce’s Crazy in Love
What makes a good statistic?
AP Exam Tips:
+ STATS MEDIC
Video 5.2 Sampling Distributions for One Population
Sample proportion Sample mean
Parameter
Statistic
Shape
Center
Varibility
z-score formula
Example 1: At a large local high school, 52% of the previous year’s graduating class enrolled in a
four-year university the following fall. The school counselors contact an SRS of 50 of the previous
year’s graduates. Find the probability that the SRS contains at least 23 students who are enrolled in a
four-year university.
Picture: Show work:
Example 2: The ACT scores a recent school year were approximately Normally distributed with a
mean of 21 and a standard deviation of 5.4. If a random sample of 5 test scores is chosen, what is
the probability that the sample mean is 25 or greater?
Picture: Show work:
AP Exam Tips:
+ STATS MEDIC
t..ideo 5.3 Sampling Distributions for Two Populations
Example 1: Two veteran sales people at a local company keep track of the proportion of sales theymake out of the number of sales meetings they have. Person A made sales at 42% of their meetings.Person B made sales at 30% of their meetings. Their manager independently selects a randomsample of 50 meetings for person A and 60 meetings for person B. Describe the samplingdistribution of
— P2
Example 2: The weights of cupcakes at a local bakery have a mean of 115 grams and a standarddeviation of 8 grams. The weights of donuts at the same bakery have a mean of 28 grams and astandard deviation of 1 2 grams. Two independent random samples of size 40 are chosen from thecupcakes and donuts. Describe the sampling distribution of 1
— 12.
Parameter
.Statistic
Shape
Center
Varibility
Two proportions Two means
AP Exam Tips:
+ STATS MEDIC
H-IVideo 6.1 One Sample Confidence Intervals
Example 1: At a local restaurant, a small order of French fries should weigh 6 oz. The restaurant
owner is concerned that her employees are filling orders of French fries improperly. She would like to
estimate the true mean weight of a small order of French fries, so she randomly selects 1 2 orders
throughout the week and weighs them. The weights are given in the table (in ounces):
6.45 6.31 5.99 6.04 5.84 7.02
6.9 6.29 6.08 5.95 6.88 6.65
Construct and interpret a 95% confidence interval to estimate the true mean weight of a small order
of French fries at this restaurant.
STATE: DO:
.
PLAN: CONCLUDE:
AP Exam Tips:
+ STATS MEDIC
Qxampie 2: The city council is considering changing an old law that prohibits people from mowingtheir lawns after 9 pm. In order to determine if the people of the city would support this change,they randomly surveyed 50 people in the city. They find that 23 of the 50 people surveyed wouldsupport changing the law.
Construct and interpret a 90% confidence interval for the true proportion of people in the city whowould support changing the law.
STATE: DO:
PLAN: CONCLUDE:
AP Exam Tips:
‘I’ STATS MEDIC
Video 6.2 Two Sample Confidence Intervals
Example 1: A pharmaceutical company is testing a new medication for cholesterol. 100 volunteers
with high cholesterol are randomly assigned to either take the new medication or the current
medication the company sells. After 6 months of use, their cholesterol level will be tested to see if
there is a difference in the proportion of people with reduced cholesterol. Thirty-nine of the 50
subjects taking the new medication had a reduction in cholesterol. Thirty-four of the 50 subjects
taking the current medication had a reduction in cholesterol.
(a) Construct and interpret a 95% confidence interval for the true difference in proportions of
people like those in the study who would have reduced cholesterol after 6 months on their
respective medication.
STATE: DO:
PLAN: CONCLUDE:
(b) Does the company have convincing evidence that there is a difference in the proportion of
people with reduced cholesterol?
+ STATS MEDIC
jxampie 2: There is a rivalry between the AP calculus students and the AP statistics students at alarge high school. They often argue about which group has the higher average SAT score. To settlethe matter, they take random samples of 10 students from each course. The sample mean from theAP calculus group has a mean of 1 320 with a standard deviation of 56, while the AP statistics grouphas a mean of 1352 with a standard deviation of 108. Both population distributions of scores can beassumed to be approximately Normal.
Construct and interpret a 99% confidence interval for the true difference in mean SAT scoresbetween the AP calc students and the AP stats students.
STATE: DO:
PLAN: CONCLUDE:
AP Exam Tips:
+ STATS MEDIC
Video 7.1 One Sample Significance Tests
Example 1: Chicago style popcorn is a type of popcorn made by mixing together cheddar and
caramel popcorn. True Chicago style popcorn is composed of at least 40% caramel popcorn. A new
popcorn shop advertises that they will be selling Chicago style popcorn. To test this claim, a
popcorn lover takes a random sample of 500 kernels of the popcorn and finds that 183 kernels are
caramel. Do the data provide convincing evidence that the shop is not selling true Chicago style
popcorn?
STATE: DO:
PLAN: CONCLUDE:
AP Exam Tips:
+ STATS MEDIC
:xample 2: Last year, an AP stats class spent an average of 25 minutes a night on their homework.
Their teacher randomly sampled 30 of her students this year to see if this average had gone up. The
sample had a mean of 32 minutes spent on homework each night and a standard deviation of 11
minutes. Do the data provide convincing evidence that AP stats students spend more time onhomework per night this year than last year?
STATE: DO:
PLAN: CONCLUDE:
AP Exam Tips:
+ STATS MEDIC
Video 7.2 Two Sample Significance Tests
Example 1: Two rival universities are both claiming that their graduates are more likely to gain
employment within 3 months of graduation than those who graduate from the other school. A
random sample of 500 recent graduates from College A revealed that 450 had employment within 3
months. A separate random sample of 400 recent graduates from College B showed that 342 had
jobs. Do the data provide convincing evidence that there is a difference in the proportion of
graduates who had employment within 3 months from College A and College B.
STATE: DO:
PLAN: CONCLUDE:
AP Exam Tips:
+ STATS MEDIC
Example 2: Last year, East Kentwood High School had 650 students take a geometry final exam. Thechool gave two forms of the exam, which were randomly assigned to the students. Half of thetudents took form A and the rest took form B. After the exam, some students claimed that form B
was more difficult than form A. To test this claim, the principal took random samples of 30 examscores from each form and recorded the score. The results are shown:
FormA n=30 =73.4 s=12.9
Form B n = 30 = 68.6 s = 15.4
Do the data provide convincing evidence that the mean score on form A was higher than the meanscore on form B using a = 0.01?
STATE: DO:
PLAN: CONCLUDE:
AP Exam Tips:
+ STATS MEDIC
Video 7.3 Difference of Means OR Mean of Differences?
Example: Two versions of the final exam.
Version A 90 82 76 88 99
Version B 83 77 79 80 81
Differences 7 5 -3 8 18
Scenario 1: Difference of Means
xA87 sA8.66
xB80 SB 2.24 XAXB7
Scenario 2: Mean of Differences
Xdff7 Sdff7.S2
AP Exam Tjpj
+ STATS MEDIC
_____
Q’ideo 7.4 Chi-Square Tests
GOODNESS OF FIT TEST TEST OF HOMOGENEITY TEST OF INDEPENDENCE
AP Exam Question
Hypotheses
Expected
Degrees of freedom
Chi-square formula
eP-value
What is the same? Draw flowchart here:
What is different?
AP Exam Tips:
+ STATS MEDIC
Video 7.5 Inference for Linear Regression
Example: A random sample of 11 high schools was selected from Michigan. The percent of students
who are free/reduced lunch and the mean SAT Math score of each high school in the sample were
recorded. Here are the data:
Line of best fit:
580
560
540
S 520S
500
480
460
440
420
400
Linear regression t-interval for slope Linear regression t-test for slope
AP Exam Tips:
+ STATS MEDIC
Percent free/reduced Mean SAT Math
East Kentwood High School 58 490.4
Rockford High School 8 535.5
Caledonia High School 18 541.3
Cedar Springs High School 39 485.9
Muskegon High School 85 427.3
Comstock Park High School 42 473.2
Sparta High School 35 483.1
Lowell High School 27 542.7
Spring Lake High School 18 554.1
Ottawa Hills High 78 402.3
Northville High School 5 597.6
0e
0
B
Percent free/iduccd lunch
Regression Analysis: Mean SAT Math score (dollars) versus Percent free/reduced lunch
Predictor Coef SE Coef T P
Constant 577.9 12.5 46.16 0.000
Percent free/reduced -1.993 0.276 -7.22 0.000lunch
S = 23.3 168 R-Sq = 85.29% R-Sq(adj) = 83.66%
I
Ofideo 7.6 Type I and Type II Errors + Power
Example: Tacos El Cunado claims that their Giant Burrito is ½ pound on average (more precisely 8.0
ounces with a standard deviation of 1 .0 ounces). Luke believes the average weight is less than that
(he thinks it is 7 ounces). To test his claim, Luke goes to Tacos El Cunado and takes a random
sample of 5 burritos. He will test his claim with an alpha level of 0.05.
H0:
HA:
Type I Error:
Interpret:
Type II Error:
terpret:
Power:
Interpret:
How to increase power?
(1)
(2)
AP Exam Tips:H0 true
Decision
Reject H0
Fail toreject H0
4’ STATS MEDIC
HA true
_—1_—
Name That Significance Test
How do I know which question is asking to do a significance test?
• (1)
• (2)
• (3)
______ ______ ______ ______
samps7(gips)2
Which Is there a Is there a Propoions2 prop ztes:
significance — Minitab _2_+ table of—---
ortest? output? frequencies? L Means?
1 1 mean t-tesHow many red t-t
samples? (groups)
______________
2 mean ttesJ
LinearX test
regression t—test
r How manysamples? (groups)
How many f X’ homogenefty]variables?
X2 GOF J X2 independence
4’ STATS MEDIC
•Jsing Your Calculator on the AP Stats Exam
Same information as 1-VarStats but for two sets ofdata.
Enter data in L1 and L22-Var Stats L1,L2
pdf and cdf
Function When to use it Input Command
binompdf To find the probability of binompdf(n, p, X)(21, VARS, DISTR) getting exactly X n: number of trials
successes. p: probability of successX: number of successes
binomcdf To find the probability of binomcdf(n, p, X)(2, VARS, DISTR) getting at most X n: number of trials
successes. p: probability of successX: number of successes
normalcdf To find area in an interval normalcdf(lower, upper, mean, SD)(2, VARS, DISTR) for a normal distribution.tcdf To find area in an interval tcdf(lower, upper, df)(2, VARS, DISTR) for a t distribution.
+ STATS MEDIC
One Variable Data
Function When to use it In put Command1-Var Stats To find mean, standard Enter data in L1 and frequency in L2 if(STAT, CALC) deviation, and 5 number needed
summary for a set of data. 1-Var Stats L1 or 1-Var Stats L11L2
Two Variable Data
Function When to use it Input Command
LinReg (a + bx) To find the equation for a Enter explanatory variable in L1(STAT, CALC) line of regression. Also Enter response variable in L2
gives correlation (r). LinReg (a + bx) L11L2
2-Var Stats(STAT, CALC)
2cdf
‘—1 (2, DISTR)
To find area in an intervalfor a x2 distribution.
2cdf(lower, upper, df)
4’ STATS MEDIC
Confidence IntervalsFunction When to use it Input Command1-PropZlnt To calculate a confidence 1-PropZlnt(STAT, TESTS, A:) interval to estimate a x: number of successes
proportion. n: sample sizeC-Level: confidence level (decimal)
Tlnterval To calculate a confidence Tlnterval(STAT, TESTS, 8:) interval to estimate a lnpt: Stats
mean. i: sample meanS: sample standard deviationn: sample sizeC-Level: confidence level (decimal)
2-PropZlnt To calculate a confidence 2-PropZlnt(STAT, TESTS, B:) interval to estimate a xl: number of successes in sample 1
difference of proportions. ni: sample size in sample 1x2: number of successes in sample 2n2: sample size in sample 2C-Level: confidence level (decimal)
2-SampTint To calculate a confidence 2-SampTint(STAT, TESTS, 0:) interval to estimate a lnpt: Stats
difference of means. 1: sample mean of sample 1Sxl: standard deviation of sample 1ni: sample size of sample 12: sample mean of sample 2Sx2: standard deviation of sample 2n2: sample size of sample 2C-Level: confidence level (decimal)Pooled: No
LinRegTlnt To calculate a confidence LinRegTlnt(STAT, TESTS, G:) interval to estimate a Enter explanatory variable in Li
slope. Enter response variable in L2*only newer Xlist: Licalculators have Ylist: L2this command* Freq: 1
C-Level: confidence level (decimal)
Qignificance Tests
Function When to use it Input Command1-PropZTest To test a claim made about 1-PropZTest
(STAT, TESTS, 5:) a single proportion. p0: null value
x: number of successes
n: sample size
Prop: po <p0 >o (alternative)
T-Test To test a claim made about T-Test
(STAT, TESTS, 2:) a single mean (standard lnpt: Stats
deviation of the population i: null value
is unknown). 1: sample mean
S: sample standard deviation
n: sample size
i: * ii < i2o > i-zo (alternative)
2-PropZTest To test a claim made about 2-PropZTest
(STAT, TESTS, 6:) a difference of proportions. xl: number of successes sample 1
ni: sample size in sample 1
x2: number of successes sample 2
n2: sample size in sample 2
p1: p2 <p2 >p2 (alternative)
2-SampTTest To test a claim made about 2-SampTTest
(STAT, TESTS, 4:) a difference of means lnpt: Stats
(standard deviation of the 1: sample mean of sample 1
populations unknown). Sxl: standard deviation sample 1
ni: sample size of sample 112: sample mean of sample 25x2: standard deviation sample 2n2: sample size of sample 2pi: p2 <p2 >p2 (alternative)
Pooled: No
+ STATS MEDIC
To test a claim made aboutthe slope of a populationregression line.
Lin RegTTestEnter explanatory variable in L1Enter response variable in L2Xlist: LiYlist: L2Freq: 1/3: 0 <0 >0 (alternative)
+ STATS MEDIC
Significance Tests - continued .Function When to use it Input Command
X2—Test To test a claim made about 2—Test(STAT, TESTS, C:) the distribution of a Enter observed values in matrix A
categorical variable.. Chi square test of Observed: [A]
association Expected: [B]. Chi square test of
homogeneity Expected values appear in matrix B
2GOF—Test To test a claim made about X2GOF—Test(STAT, TESTS, D:) the distribution of a Enter observed values in Li
categorical variable. Enter expected values in L2*i..iIy newer . Chi square goodness- Observed: Licalculators have of-fit test Expected: L2this command* df: degrees of freedom
Li n RegTTest(STAT, TESTS, E:)
Know Your AP Stats Formula Sheet
Page 1
What categories of formulas appear on this page?
Important notes:
Page 2
What categories of formulas appear on this page?
Important notes:
+ STATS MEDIC
How to CRUSH the AP Stats Free Response
Strategy #1: Know What to Expect
• 1-variable stats
• 2-variable stats
• Sampling methods or experimental design
• Probability
• Significance test
• Investigative Task
Strategy #2: Survive the Investigative Task
• 25% of free response grade
• New stuff!
• 4to5parts
• Parts are scaffolded
Strategy #3: Have a Plan
• 90 minutes for 6 questions
• Take a practice test
• Two approaches:
o
o 1 - significance test - 6 - probability - others
Strategy #4: Get All Your Points!
• Don’t leave any blank
• Make up an answer
• Always use context
+ STATS MEDIC
How to Survive the Investigative Task
Know the Facts
.
.
.
Use These Strategies
.
.
2019 AP Statistics Exam FRQ #6
Write the highlighted text from each part.
(a)
(b)
(c)
(d)
(e)
(f)
AP Exam Tips:
+ STATS MEDIC
HTop 10 AP Stats Exam Tips
1: Clearly communicate your understanding
2: Always include context in your answers
3: Be precise in your language and vocabulary
4: Use appropriate notation
5: Do not rely on your calculator
6: Manage your time
7: Do not leave anything blank
8: Know the formula sheet
9: Know your inference
10: Be confident!
+ STATS MEDIC
——H— .. H ———•••iQJnit 1 Free Response 2015 #1
1. Two large corporations, A and B, hire many new college graduates as accountants at entry-level positions. In2009 the starting salary for an entry-level accountant position was $36,000 a year at both corporations. At eachcorporation, data were collected from 30 employees who were hired in 2009 as entry-level accountants and werestill employed at the corporation five years later. The yearly salaries of the 60 employees in 2014 aresummarized in the boxplots below.
$30 $40 $50 $60 S70 $80
Yearly Salary (thousands)
(a) Write a few sentences comparing the distributions of the yearly salaries at the two corporations.
(b) Suppose both corporations offered you ajob for $36,000 a year as an entry-level accountant.
(i) Based on the boxplots, give one reason why you might choose to accept the job at corporation A.
(ii) Based on the boxplots, give one reason why you might choose to accept the job at corporation B.
Source: Copyright © The College Board.*AP is a registered trademark of the College Board, which was not involved in the production of,
and does not endorse, this product.all STATS MEDIC
Corporation A
Corporation B
* *
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ndi
stan
cebe
twee
nea
chin
divi
dual
grad
eof
the
mid
term
exam
s.
(D)
App
roxi
mat
ely
the
mea
ndi
stan
cebe
twee
nth
ein
divi
dual
grad
esof
the
mid
term
exam
san
dth
e
mea
ng
rad
eof
all
mid
term
exam
s.(E
)A
ppro
xim
atel
yth
em
edia
ndi
stan
cebe
twee
nth
ein
divi
dual
grad
esof
the
mid
term
exam
san
dth
e
med
ian
gra
de
ofal
lm
idte
rmex
ams.
+ST
ATS
MED
IC
.,.
111
105
98 96 93
ISI 80
82
4.C
onsi
der
the
stem
plot
belo
w,
whi
chgi
ves
the
num
ber
ofpe
ople
atte
ndin
ga
mat
inee
show
atth
elo
cal
mov
ieth
eatr
efo
rth
epa
st26
days
.
6 7 8 9 10 11 12
8 025
0357
11
28
3558
Key
:11
8=
18peo
ple
Whi
chof
the
foll
owin
gst
atem
ents
are
true
?
I.T
hefi
venu
mbe
rsu
mm
ary
is18
,35
,54
,87
,12
3II.
Hal
fof
the
data
valu
esar
ela
rger
than
54.
Ill.
The
shap
eof
the
dist
ribu
tion
issk
ewed
left
.
(A)
Iand
II(B
)II
(C)
IIan
dIII
(D)
Ill(E
)I,
II,an
dIll
.
...
...........................................,....
.,,,.
6.A
dist
ribu
tion
has
ash
ape
that
isst
rong
lysk
ewed
left
.W
hich
ofth
efo
llow
ing
stat
emen
tsis
mos
t
likel
ytr
ueab
out
this
dist
ribu
tion
?
(A)
Mea
n>
Med
ian.
(B)
Mea
n=
Med
ian.
(C)
Mea
n<
Med
ian.
(D)
Onl
yth
em
ode
can
bede
term
ined
.(E
)T
here
are
noou
tlie
rsin
the
dist
ribu
tion
.
7.S
ever
alst
uden
tsin
anA
PS
tati
stic
scl
ass
adm
inis
ter
asu
rvey
toa
sam
ple
ofst
uden
tsin
thei
r
scho
ol,
aski
ngth
est
uden
tsho
wfa
rth
eytr
avel
tosc
hool
inm
iles.
Whi
chof
the
follo
win
gst
atis
tics
wou
ldno
tbe
mea
sure
din
mile
s?
(A)
Mea
n(B
)M
edia
n(C
)ln
terq
uart
ile
rang
e(D
)S
tand
ard
devi
atio
n
(E)
Var
ianc
e
8.T
hefo
llow
ing
tabl
esh
ows
how
high
scho
olst
uden
tsin
four
grad
ele
vels
ate
thei
rlu
nch
ona
part
icul
arda
y—
purc
hase
din
the
cafe
teri
a,br
ough
ta
bag
lunc
h,or
purc
hase
dlu
nch
off
cam
pus.
Wha
tis
the
appr
oxim
ate
prop
orti
onof
Juni
ors
that
purc
hase
dlu
nch
off-
cam
pus
onth
ispa
rtic
ular
day?
Fre
shm
anS
opho
mor
eJu
nior
Sen
ior
Caf
eter
ia65
7050
30
Bag
ged
Lun
ch12
010
070
60
Off
-Cam
pus
020
4565
5.W
hich
ofth
efo
llow
ing
stat
emen
tsis
true
?
(A)
His
togr
ams
have
gaps
betw
een
each
bar.
(B)
Dot
plot
sdo
not
prov
ide
enou
ghin
form
atio
nto
dete
rmin
eif
ther
ear
eou
tlie
rsin
the
data
.
(C)
Bar
grap
hsca
ndi
spla
ybo
thqu
anti
tati
vean
dca
tego
rica
lda
ta.
(D)
Ste
mpl
ots
are
the
best
grap
hsfo
rdi
spla
ying
data
sets
with
two
vari
able
s.
(E)
Box
plot
scl
earl
ysh
owth
efi
ve-n
umbe
rsu
mm
ary
ofa
data
set.
(A)
0.06
(B)
0.37
(C)
0.24
(D)
0.27
(E)
0.35
3 4 53 1
917
22
7 3
4’ST
ATS
MED
IC+
STAT
SM
EDIC
9.A
club
bow
ling
team
has
12m
embe
rs.
The
firs
tte
nm
embe
rsbo
wl
aga
me,
and
thei
rav
erag
e
scor
eis
156.
Ifyo
ukn
owth
ene
xttw
om
embe
rsbo
wl
scor
esof
173
and
151,
doyo
uha
veen
ough
info
rmat
ion
tofi
ndth
eto
tal
ofal
l12
scor
es?
(A)
Yes
,th
eto
tal
is15
7.(B
)Y
es,
the
tota
lis
1872
.(C
)Y
es,
the
tota
lis
1884
.(D
)N
o,w
ew
ould
need
tokn
owth
ete
nin
divi
dual
scor
es.
CE)
No,
we
wou
ldne
edto
know
the
stan
dard
devi
atio
n.
10.
The
mos
aic
plot
show
sth
edi
stri
buti
onof
favo
rite
mat
hcl
ass
for
stud
ents
and
teac
hers
atE
ast
Ken
twoo
dH
igh
Sch
ool.
Bas
edon
the
grap
h,w
hich
ofth
efo
llow
ing
stat
emen
tsis
true
?
(A)
The
rear
em
ore
teac
hers
than
stud
ents
who
chos
eth
eir
favo
rite
mat
hcl
ass
asA
PC
aIc.
(B)
100%
ofst
uden
tsch
ose
Intr
oS
tats
asth
eir
favo
rite
mat
hcl
ass.
(C)
Whe
nco
mbi
ning
stud
ents
and
teac
hers
,A
PS
tats
has
the
high
est
over
all
prop
orti
onw
ho
chos
eit
asth
eir
favo
rite
mat
hcl
ass.
(D)
80%
ofst
uden
tsch
ose
AP
Ca
Ic.
(E)
The
rear
em
ore
teac
hers
than
stud
ents
atE
ast
Ken
twoo
dH
igh
Sch
ool.
intr
oSt
ats
Pre-
Cal
e—
AP
CaI
c•
AP
Sta
ts
Ca
6o
.o%
j
I
+ST
ATS
MED
IC
..
.
zzLJzJj
Gnit 1 Practice Free Response Question
Below are boxplots that summarize the weights (in pounds) of large samples from two breeds ofdog: the Anatolian Shepherd and the Black Russian Terrier.
Anatolian Shepherd
Black Russian Terrier
80 90 100 110 120 130Weight (pounds)
1•0 10 10 1’’0
(a) Compare the distributions of weights for the two dog breeds.
(b) This sample of Black Russian Terriers does not contain any outliers. What weights would aBlack Russian Terrier have to be to be considered an outlier?
+ STATS MEDIC
F 1
Unit 2 Free Response 2017 #1
1. Researchers studying a pack of gray wolves in North America collected data on the length x, in meters, from
nose to tip of tail, and the weight y, in kilograms, of the wolves. A scatterplot of weight versus length revealed
a relationship between the two variables described as positive, linear, and strong.
(a> For the situation described above, explain what is meant by each of the following words.
(i) Positive:
(ii) Linear:
(iii) SIrQng
.The data collected from the wolves were used to create the least-squares equation 9 = —16.46 + 35 .02x.
(b) Interpret the meaning of the slope of the least-squares regression line in context.
(c) One wolf in the pack with a length of 1.4 meters had a residual of —9.67 kilograms. What was the weight
of the wolf?
Source; Copyright © The College Board.*AP is a registered trademark of the College Board, which was not involved in the production of,
and does not endorse, this product.
Uni
t2
Mul
tipl
eC
hoic
e
1.W
hich
ofth
efo
llow
ing
rela
tion
ship
sbe
twee
ntw
ova
riab
les
coul
dbe
desc
ribe
dus
ing
corr
elat
ion,
r? (A)
Num
ber
ofbo
oks
read
and
gen
der
ofa
stud
ent.
(B)
Num
ber
offo
otba
llga
mes
play
edan
dth
epo
siti
onof
afo
otba
llpl
ayer
.
(C)
Hig
hte
mp
erat
ure
ofth
eda
yan
dnu
mbe
rof
zoo
visi
tors
that
day.
(D)
Typ
eof
beve
rage
orde
red
and
tim
eof
day
itw
asor
dere
d.
(E)
Bra
ndof
cell
phon
ean
dnu
mbe
rof
cell
phon
esso
ld.
2.A
scat
terp
lot
show
sa
stro
ng,
posi
tive
,li
near
rela
tion
ship
betw
een
the
num
ber
ofre
boun
dsa
bask
etba
llte
amav
erag
esan
dth
enu
mbe
rof
win
sth
atte
amre
cord
sin
ase
ason
.W
hich
conc
lusi
onis
mos
tap
prop
riat
e?
(A)
Ate
amth
atin
crea
ses
itsnu
mbe
rof
rebo
unds
caus
esits
chan
ces
ofw
inni
ngm
ore
gam
esto
incr
ease
.(B
)If
the
resi
dual
plot
show
sno
patt
ern,
then
itis
safe
toco
nclu
deth
atge
ttin
gm
ore
rebo
unds
caus
esm
ore
win
s,on
aver
age.
(C)
Ifth
ere
sidu
alpl
otsh
ows
nopa
tter
n,th
enit
issa
feto
conc
lude
that
gett
ing
mor
ew
ins
caus
es
mor
ere
boun
ds,
onav
erag
e.(D
)If
the
r2va
lue
iscl
ose
enou
ghto
100%
,th
enit
issa
feto
conc
lude
that
gett
ing
mor
ere
boun
ds
caus
esm
ore
win
s,on
aver
age.
(E)
Reb
ound
san
dw
ins
are
posi
tive
lyco
rrel
ated
,bu
tw
eca
nnot
conc
lude
that
gett
ing
mor
e
rebo
unds
caus
esm
ore
win
s,on
aver
age.
3.T
wo
vari
able
s,x
andy,
have
aco
rrel
atio
nof
0.75
.If
xha
sa
mea
nof
25an
da
stan
dard
devi
atio
n
of3,
andy
has
am
ean
of12
and
ast
anda
rdde
viat
ion
of6,
whi
chof
the
follo
win
gis
the
leas
t-
squa
res
regr
essi
onlin
efo
rth
etw
ova
riab
les?
(A)
9—
25.5
+1.
5x(B
)9
=12
+1.
5x(C
)9
=12
+0.
75x
(D)
916
÷0.
75x
(E)
Not
enou
ghin
form
atio
n
...
4.D
ata
are
coll
ecte
don
the
amou
ntof
fat
(ingr
ams)
and
calo
ries
inth
efr
ench
fry
orde
rsat
nine
fast
food
rest
aura
nts.
The
leas
t-sq
uare
sre
gres
sion
line
for
the
data
is9
274.
34+
9.55
x,w
here
9is
the
pred
icte
dnu
mbe
rof
calo
ries
and
xis
gram
sof
fat.
Whi
chof
the
follo
win
gis
the
corr
ect
inte
rpre
tati
onof
the
slop
eof
the
leas
t-sq
uare
sre
gres
sion
line?
(A)
The
calo
ries
incr
ease
by9.
55,
onav
erag
e.
(B)
For
ever
yin
crea
sein
fat,
the
calo
ries
incr
ease
asw
ell.
(C)
Eve
ryin
crea
seof
1gr
amof
fat
caus
esan
incr
ease
of9.
55ca
lori
es.
(D)
For
ever
yin
crea
seof
1gr
amof
fat,
the
pred
icte
dca
lori
esin
crea
seby
9.55
.
(E)
For
ever
yin
crea
seof
1ca
lori
e,th
epr
edic
ted
gram
sof
fat
incr
ease
by9.
55.
5.T
hesc
atte
rplo
tbe
low
show
sda
tafo
rth
eni
nefr
ench
fry
orde
rsfr
omth
epr
evio
uspr
oble
m,
with
the
leas
t-sq
uare
sre
gres
sion
line
disp
laye
d.W
hich
ofth
efo
llow
ing
isth
ebe
stes
tim
ate
ofth
eva
lue
ofth
ere
sidu
alfo
rth
epo
int
indi
cate
dby
the
arro
w?
(A)
-570
(B)
570
(C)
-60
(D)
60(E
)63
0
.,
620
560
5) 50
0 440
380
812
1620
2428
3236
fat
4.ST
ATS
MED
IC+
STAT
SM
EDIC
6.T
hesc
atte
rplo
tbe
low
show
sda
tafo
rth
eni
nefr
ench
fry
orde
rsfr
omth
epr
evio
uspr
oble
m.
Ate
nth
fast
food
chai
nha
sbe
enad
ded
,as
indi
cate
dby
the
arro
w.
How
wou
ldth
iste
nth
data
poin
taf
fect
the
slop
ean
dco
rrel
atio
nin
this
scen
ario
?
•.28
1216
2024
2832
36fa
t
(A)
Slo
pede
crea
ses,
corr
elat
ion
incr
ease
s(B
)S
lope
incr
ease
s,co
rrel
atio
nin
crea
ses
(C)
Slo
pein
crea
ses,
corr
elat
ion
dec
reas
es(D
)S
lope
decr
ease
s,co
rrel
atio
nd
ecre
ases
(E)
Can
not
bede
term
ined
wit
hout
the
full
set
ofda
ta
7.B
atte
rylif
eha
sa
stro
ng,
nega
tive
,li
near
rela
tion
ship
with
tem
pera
ture
.If
the
leas
t-sq
uare
sre
gres
sion
line
usin
gx
=te
mp
erat
ure
expl
ains
90%
ofth
eva
riat
ion
inba
tter
ylif
e,w
hich
ofth
efo
llow
ing
mus
tbe
the
corr
elat
ion,
r,be
twee
nba
tter
ylif
ean
dte
mpe
ratu
re?
(A)
-0.9
0(8
)0.
90(C
)-0
.95
(D)
0.95
(E)
Can
not
bede
term
ined
wit
hout
the
orig
inal
data
.
8.A
rand
omsa
mpl
eof
hous
ehol
dsis
take
n.Fo
rea
chho
useh
old,
the
num
ber
ofho
urs
spen
t
wat
chin
gte
levi
sion
and
the
pow
erco
nsum
ptio
n(in
kWh)
duri
nga
day
are
reco
rded
.T
heta
ble
belo
wsh
ows
com
pute
rou
tput
from
ali
near
regr
essi
onan
alys
ison
the
data
.
Pre
dict
orC
oef
SEC
oef
TP
Con
stan
t19
.31
2.86
216.
750.
000
Hou
rste
levi
sion
0.89
10.
2715
3.28
0.00
2
54.
185
R-S
q=
30.0
%R
-Sq(
adj)
=28
.9%
Whi
chof
the
foll
owin
gis
the
equa
tion
ofth
ele
ast-
squa
res
regr
essi
onlin
e?
(A)
2=
19.3
1+
0.89
1x
(B)
2=
2.86
21+
0.27
15x
(C)
2=
0.89
1+
19.3
1x(D
)2
=0.
2715
+2.
8621
x(E
)=
0.27
15+
0.89
1x
9.A
rand
omsa
mpl
eof
hous
ehol
dsis
take
n.Fo
rea
chho
useh
old,
the
num
ber
ofho
urs
spen
tw
atch
ing
tele
visi
onan
dth
epo
wer
cons
umpt
ion
(inkw
h)du
ring
ada
yar
ere
cord
ed.
The
tabl
ebe
low
show
sco
mpu
ter
outp
utfr
oma
line
arre
gres
sion
anal
ysis
onth
eda
ta.
Pre
dict
orC
oef
SEC
oef
TP
Con
stan
t19
.31
2.86
216.
750.
000
Hou
rste
levi
sion
0.89
10.
2715
3.28
0.00
2
S=
4.18
5R
-Sq
30.0
%R
-Sq(
adj)
=28
.9%
Whi
chof
the
foll
owin
gis
aco
rrec
tin
terp
reta
tion
ofr2
?
(A)
Num
ber
ofho
urs
ofte
levi
sion
expl
ains
30%
ofth
eva
riab
ility
inpo
wer
cons
umpt
ion.
(B)
30%
ofth
ein
crea
sein
num
ber
ofho
urs
ofte
levi
sion
isex
plai
ned
bypo
wer
cons
umpt
ion.
(C)
30%
ofth
eda
taw
illlie
onth
ele
ast-
squa
res
regr
essi
onlin
e.
(D)
30%
ofth
ere
sidu
als
will
bele
ssth
an4.
185.
(E)
All
ofth
eab
ove
are
corr
ect
inte
rpre
tati
ons
620
,,56
0-C 500 440
380
+ST
ATS
MED
IC
.
‘4’ST
ATS
MED
IC
...
—
a-I—
I—
Unit 2 Practice Free Response Question
The computer output below gives results from the linear regression analysis for predicting the
pounds of fuel consumed based on the distance traveled in miles for passenger aircraft. Data usedfor this analysis were obtained from ten randomly selected flights.
Predictor Coef SE Coef T PConstant -4702.64 1657 -2.84 0.022Distance (miles) 21.282 0.833 25.54 0.000
S = 2766.57 R-Sq = 98.8% R-Sq(adj)=98.3%
(a) What is the equation of the least-squares regression line that describes the relationship between
the distance traveled in miles and the pounds of fuel consumed? Define any variables used in thisequation.
(b) Below is a residual plot for the ten flights. Is it appropriate to use the linear regression equation
to make predictions? Explain.
6000
0
I aS
U-6000 —
(c) Interpret the y-intercept in the context of the problem. Is this value statistically meaningful?
+ STATS MEDIC
O1t 3 Free Response 2016 #3
3. Alzheimer’s disease results in a loss of cognitive ability beyond what is expected with typical aging. A localnewspaper published an article with the following headline.
Study Finds Strong Association Between Smoking and Alzheimer’s 1The article reported that a study tracked the medical histories of 21,123 men and women for 23 years.The article stated that, for those who smoked at least two packs of cigarettes a day, the risk of developingAlzheimer’s disease was 2.57 times the risk for those who did not smoke.
(a) Identify the explanatory and response variables in the study.
Explanatory variable:
Response variable:
(b) Is the study described in the article an observational study or an experiment? Explain.
(c) Exercise status (regular weekly exercise versus no regular weekly exercise) was mentioned in the article as apossible confounding variable. Explain how exercise status could be a confounding variable in the study.
Source: Copyright © The College Board.*Ap is a registered trademark of the College Board, which was not involved in the production of,
and does not endorse, this product. + STATS MEDIC
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6.T
heD
epar
tmen
tof
Nat
ural
Res
ourc
es(D
NR
)is
plan
ning
ast
udy
tode
term
ine
whe
ther
brea
kwat
ers
help
dec
reas
eer
osio
nat
ala
rge
lake
.T
hey
divi
deth
esh
orel
ine
into
100-
foot
plot
s,
inst
allin
gso
me
with
brea
kwat
ers
and
som
ew
itho
ut.
How
ever
,th
eea
stan
dw
est
shor
elin
esof
this
lake
rece
ive
very
diff
eren
tw
ave
patt
erns
due
toth
ew
ind.
The
DN
Rsu
spec
tsth
isw
illaf
fect
the
resp
onse
sto
the
brea
kwat
ers.
Bec
ause
ofth
is,
the
DN
Rpl
ans
totr
eat
each
shor
elin
eas
adi
ffer
ent
grou
p.T
his
stud
yis
anex
ampl
eof
(A)
An
unco
ntro
lled
expe
rim
ent.
(B)
Abl
ocke
dde
sign
expe
rim
ent.
(C)
Am
atch
edpa
irs
expe
rim
ent.
(D)
Ast
rati
fied
rand
omsa
mpl
e.
(E)
Ara
ndom
ized
obse
rvat
iona
lst
udy.
7.Fo
rty
adul
tm
ales
volu
ntee
red
topa
rtic
ipat
ein
anex
peri
men
t.H
alf
ofth
emar
era
ndom
lyas
sign
ed
tota
kea
caff
eine
supp
lem
ent
befo
rew
orki
ngou
t,an
dth
eot
her
half
are
assi
gned
tota
kea
plac
ebo
befo
reco
mpl
etin
gth
esa
me
wor
kout
.D
urin
gth
ew
orko
ut,
hear
tra
tem
onit
ors
will
beus
edto
mea
sure
each
part
icip
ant’
she
art
rate
.T
hest
udy
foun
dth
atth
ose
who
took
aca
ffei
nesu
pple
men
t
had
sign
ific
antl
yhi
gher
aver
age
puls
era
tes
duri
ngth
ew
orko
ut.
Wha
tco
nclu
sion
can
bedr
awn
from
the
stud
y?
(A)
Tw
oex
peri
men
tal
grou
psof
20ea
chis
too
smal
lto
conc
lude
that
the
resu
lts
are
sign
ific
ant.
(B)
Tho
seth
atto
okth
eca
ffei
nesu
pple
men
tha
da
high
erav
erag
ehe
art
rate
duri
ngth
ew
orko
ut,
but
itw
ould
not
beco
rrec
tto
conc
lude
that
caff
eine
caus
edth
isto
occu
r.
(C)
The
caff
eine
supp
lem
ents
caus
edth
ehe
art
rate
sto
incr
ease
due
toth
epl
aceb
oef
fect
.
(D)
Caf
fein
esu
pple
men
tsw
ill,
onav
erag
e,ra
ise
the
hear
tra
tes
ofal
lad
ult
mal
esdu
ring
aw
orko
ut
sim
ilar
toth
eon
epe
rfor
med
inth
eex
peri
men
t.
(E)
Caf
fein
esu
pple
men
tsw
ill,
onav
erag
e,ra
ise
the
hear
tra
tes
ofad
ult
mal
essi
mila
rto
thos
ein
this
stud
ydu
ring
aw
orko
utsi
mila
rto
the
one
perf
orm
edin
the
expe
rim
ent.
.8.
The
foll
owin
g8
truc
km
odel
sw
illbe
used
inan
expe
rim
ent w
ithtw
otr
eatm
ents
.T
hetr
ucks
are
list
edac
cord
ing
toth
eir
mak
ean
dsi
ze.
Ifth
eex
peri
men
tus
esa
bloc
kde
sign
base
don
the
size
of
the
truc
ks,
whi
chof
the
foll
owin
gis
not
apo
ssib
lelis
tof
truc
ksth
atre
ceiv
eth
efi
rst
trea
tmen
t?
Mid
-siz
eF
ull
-siz
e
Chev
yC
olor
ado
Sil
vera
do
GM
CC
anyo
nSi
erra
Nis
san
Fro
ntie
rT
itan
To
yo
taT
acom
aT
undr
a
(A)
Col
orad
o,Si
erra
,F
ront
ier,
Tun
dra
(B)
Col
orad
o,C
anyo
n,T
itan,
Tac
oma
(C)
Col
orad
o,S
ilve
rado
,C
anyo
n,Si
erra
(D)
Can
yon,
Fro
ntie
r,T
itan,
Tun
dra
(E)
Sil
vera
do,
Fro
ntie
r,T
itan,
Tac
oma
9.D
iver
ticul
itis
isa
com
mon
inte
stin
alai
lmen
t.T
ote
sta
new
med
icat
ion,
aho
spit
alta
kes
50
volu
ntee
rsw
hoha
vea
mod
erat
eca
seof
the
dise
ase.
The
volu
ntee
rsar
era
ndom
lyas
sign
edto
two
trea
tmen
tgr
oups
,on
ere
ceiv
ing
the
old
med
icat
ion
and
one
rece
ivin
gth
ene
wm
edic
atio
n.T
hepi
lls
are
dist
ribu
ted
inun
mar
ked
pill
form
soth
atth
epa
tien
tsan
dm
edic
alpr
ofes
sion
als
dono
tkn
ow
whi
chm
edic
atio
nth
epa
tien
tis
taki
ng.
Whi
chof
the
foll
owin
gst
atem
ents
is/a
retr
ue?
(A)
Ill
I.If
the
resu
lts
show
that
the
new
med
icat
ion
issi
gnif
ican
tlym
ore
effe
ctiv
eth
anth
eol
d
med
icat
ion,
we
can
conc
lude
that
the
new
med
icat
ion
will
bem
ore
effe
ctiv
efo
ral
lpe
ople
that
have
am
oder
ate
case
ofth
edi
seas
e.
II.T
hegr
oup
rece
ivin
gth
eol
dm
edic
atio
nse
rves
asa
cont
rol
grou
p.
Ill.
Thi
sis
anex
ampl
eof
ado
uble
-bli
ndex
peri
men
t.
(B)
Iand
II
(C)
Iand
Ill(D
)II
and
Ill(E
)I,
II,an
dIll
+ST
ATS
MED
IC+
STAT
SM
EDIC
10.
Ast
udy
isco
nduc
ted
tode
term
ine
ifth
ebl
uelig
htfr
oma
tab
let
devi
cew
illaf
fect
the
fall
asle
epti
me
ofpe
ople
inva
riou
sag
egr
oups
diff
eren
tly.
Vol
unte
ers
for
the
stud
yar
eg
rou
ped
byag
e:18
-30
,31
-50,
and
50+
.H
alf
ofea
chgr
oup
isas
sign
eda
stan
dard
tabl
et,
the
othe
rha
lfis
assi
gned
ata
ble
tw
ithre
duce
dbl
uelig
ht.
Peo
ple
inea
chgr
oup
are
aske
dto
use
the
tab
let
for
10m
inut
esbe
fore
bed
and
thei
rfa
llas
leep
tim
eis
reco
rded
.W
hich
ofth
efo
llow
ing
isco
rrec
t?
(A)
Blo
cks:
the
thre
eag
egr
oups
.T
reat
men
ts:
usin
gth
est
anda
rdta
ble
tor
the
redu
ced
blue
ligh
tta
ble
tbe
fore
bed.
Res
pons
eva
riab
le:
How
the
eyes
reac
tto
blue
light
.(B
)B
lock
s:th
eth
ree
age
grou
ps.
Tre
atm
ents
:m
easu
ring
how
long
itta
kes
tofa
llas
leep
.R
espo
nse
vari
able
:T
heho
urs
ofsl
eep
reco
rded
.
(C)
Str
ata:
the
thre
eag
egr
oups
.T
reat
men
ts:
usin
gth
est
anda
rdta
ble
tor
the
redu
ced
blue
light
tab
let
befo
rebe
d.R
espo
nse
vari
able
:H
owth
eey
esre
act
tobl
uelig
ht.
(D)
Blo
cks:
the
thre
eag
egr
oups
.T
reat
men
ts:
usin
gth
est
anda
rdta
ble
tor
the
redu
ced
blue
light
tab
let
befo
rebe
d.R
espo
nse
vari
able
:T
ime
itta
kes
tofa
llas
leep
.(E
)B
lock
s:th
egr
oup
rece
ivin
gth
est
anda
rdta
ble
tan
dth
egr
oup
rece
ivin
gth
ere
duce
dbl
uelig
htta
blet
.T
reat
men
ts:
usin
gth
est
anda
rdta
ble
tor
the
redu
ced
blue
ligh
tta
ble
tbe
fore
bed.
Res
pons
eva
riab
le:
Tim
eit
take
sto
fall
asle
ep.
ilimST
ATS
MED
IC
..
.
Jnit 3 Practice Free Response Question
The two tires on a bicycle experience wear much in the same way car tires do; repeated contact with the roador sidewalk will wear down the raised rubber, giving the tire less traction. A major tire manufacturer hasdeveloped a new bicycle tire design they hope will reduce wear. After running several rounds of testing inlaboratory conditions, they want to test the tires in real-life biking conditions. They find 20 volunteers whobike on a daily basis. The volunteers are each given a new bike of the same model for the duration of theexperiment. The volunteers are to bike as they normally would for a month, then return the bike to have thewear of the tires measured, determined by millimeters of tire depth remaining. The manufacturer knowsthese results must be compared to their standard model tire, so they will use the standard model in theexperiment as a control group.
a) The manufacturer determines a matched pair design would be most appropriate to compare the wear ofthe new tire design to the standard design. Describe how to implement a matched pair design for thisexperiment.
b) Describe the primary advantage of using a matched pair design in the context of this experiment.
c) At the conclusion of the experiment, the manufacturer finds that the new tire design has experiencedstatistically significantly less wear than the standard tire design. Can the manufacturer infer that the new tirewill cause significantly less tire wear for all bikers? Explain.
+ STATS MEDIC
__________
I
Unit 4 Free Response 2017 #3
3. A grocery store purchases melons from two distributors, J and K. Distributor 3 provides melons from organicfarms. The distribution of the diameters of the melons from Distributor J is approximately normal with mean133 millimeters (mm) and standard deviation 5 mm.
(a) For a melon selected at random from Distributor J, what is the probability that the melon will have adiameter greater than 137 mm?
Distributor K provides melons from nonorganic farms. The probability is 0.8413 that a melon selected at randomfrom Distributor K will have a diameter greater than 137 mm. For all the melons at the grocery store, 70 percentof the melons are provided by Distributor J and 30 percent are provided by Distributor K.
(b) For a melon selected at random from the grocery store, what is the probability that the melon will have adiameter greater than 137 mm?
(c) Given that a melon selected at random from the grocery store has a diameter greater than 137 mm, what isthe probability that the melon will be from Distributor 3?
Source: Copyright © The College Board.*Ap is a registered trademark of the College Board, which was not involved in the production of,
and does not endorse, this product.
Uni
t4M
ulti
ple
Cho
ice
1.In
the
casi
noga
me
Rou
lett
e,a
bet
on“r
ed”
will
win
ifth
eba
llla
nds
onon
eof
the
18re
dnu
mbe
rs
ofth
e38
num
bers
onth
ew
heel
,w
ithea
chnu
mbe
rbe
ing
equa
lly
likel
y.Y
ouw
ant
toru
na
sim
ulat
ion
that
will
esti
mat
eth
epr
obab
ilit
yof
apl
ayer
win
ning
both
bets
whe
nbe
ttin
gon
red
twic
e.W
hich
of
the
foll
owin
gw
ould
bean
appr
opri
ate
setu
pfo
rth
esi
mul
atio
n:
I.U
sea
tabl
eof
rand
omdi
gits
tose
lect
one
num
ber
from
01to
38an
dth
ena
seco
nd
num
ber
from
01to
38.
Ifth
efi
rst
num
ber
isbe
twee
n01
and
18an
dth
ese
cond
num
ber
isbe
twee
n01
and
18,
then
the
play
erha
sw
onbo
thro
unds
.
II.U
sea
tabl
eof
rand
omdi
gits
tose
lect
two
num
bers
01-3
8,w
itho
utre
peat
s.If
both
num
bers
are
betw
een
01an
d18
,th
enth
epl
ayer
has
won
both
roun
ds.
Ill.
Use
ata
ble
ofra
ndom
digi
tsto
sele
cttw
onu
mbe
rs01
-19,
allo
win
gre
peat
s.If
both
num
bers
are
betw
een
01an
d09
,th
enth
epl
ayer
has
won
both
roun
ds.
(A)
I(B
)II
(C)
III(D
)Ia
ndII
(E)
I and
III
2.A
ta
sum
mer
cam
p,72
%of
the
cam
pers
part
icip
ate
inro
pecl
imbi
ngan
d26
%pa
rtic
ipat
ein
cano
eing
.83
%of
the
cam
pers
part
icip
ate
inro
pecl
imbi
ng,
cano
eing
,or
both
.W
hat
isth
e
prob
abil
ity
that
ara
ndom
lyse
lect
edca
mpe
rpa
rtic
ipat
esin
both
rope
clim
bing
and
cano
eing
?
(A)
0.11
(B)
0.15
(C)
0.69
(D)
0.98
(E)
Can
not
bede
term
ined
. 3.T
heta
ble
belo
wgi
ves
info
rmat
ion
onth
enu
mbe
rof
hous
esbu
ilt
inth
ree
diff
eren
tne
ighb
orho
ods
and
inth
ree
diff
eren
tde
cade
s.W
hich
one
ofth
efo
llow
ing
stat
emen
tsis
fals
e?
1960
s19
70s
1980
s
Sha
dyL
ane
4030
10
Oak
cres
t60
155
Pin
ewoo
dE
stat
es0
4515
(A)
Hou
ses
inP
inew
ood
Est
ates
and
hous
esbu
iltin
the
1960
sar
em
utua
lly
excl
usiv
e.
(B)
The
even
ts“h
ome
isin
Oak
cres
t”an
d“h
ome
was
buil
tin
1970
s”ar
edep
enden
t.
(C)
Ifa
hous
eis
sele
cted
atra
ndom
,th
epr
obab
ilit
yth
atth
eho
use
was
buil
tin
the
1980
sis
30/2
20.
(D)
The
prob
abil
ity
that
ara
ndom
lyse
lect
edho
me
was
buil
tin
the
1980
sor
isin
the
Oak
cres
t
neig
hbor
hood
is11
0/22
0.
(E)
The
prob
abil
ity
that
ara
ndom
lyse
lect
edho
use
inS
hady
Lan
ew
asbu
iltin
the
1960
sis
1/2
.
4.A
ccor
ding
tosc
hool
reco
rds,
your
scho
ol’s
soft
ball
team
win
s62
%of
the
tim
ew
hen
they
play
a
gam
eon
thei
rho
me
fiel
dan
d26
%of
the
tim
ew
hen
they
play
atth
eot
her
team
’sfi
eld.
Thi
sse
ason
,
they
play
45%
ofth
eir
gam
esat
thei
rho
me
fiel
d.A
ssum
ing
this
team
win
sat
the
sam
epa
ceas
prev
ious
team
s,w
hat
isth
epr
obab
ilit
yth
atth
eyw
ina
rand
omly
sele
cted
gam
eth
isse
ason
?
(A)
0.04
0(B
)0.
143
(C)
0.27
9CD
)0.
422
(E)
0.44
0
5.R
edun
dant
mon
itor
ing
mea
nsth
ata
sign
alis
sent
inm
ulti
ple
form
sor
path
sto
reac
hits
inte
nded
targ
et.
For
exam
ple,
anal
arm
may
bese
tup
tose
ndm
ulti
ple
sign
als
toa
secu
rity
com
pany
,ea
ch
ind
epen
den
tof
each
othe
rin
case
offa
ilure
alon
gon
epa
th.
Ifan
alar
mse
nds
off
four
sign
als
dow
n
diff
eren
tpa
ths,
and
each
has
a0.
65pr
obab
ilit
yof
reac
hing
the
secu
rity
com
pany
,w
hat
isth
e
prob
abil
ity
that
atle
ast
one
sign
alsu
cces
sful
lyre
ache
sth
ese
curi
tyco
mpa
ny?
(A)
0.01
5(B
)0.1
11
(C)
0.17
8(D
)0.
821
(E)
0.98
5
.
+ST
ATS
MED
IC+
STAT
SM
EDIC
6.A
com
pany
adve
rtis
estw
oca
rti
rem
odel
s.T
henu
mbe
rof
thou
sand
sof
mile
sth
atth
est
anda
rd
mod
elti
res
last
has
am
ean
Ps=
60an
dst
anda
rdde
viat
ion
S5.
The
num
ber
ofm
iles
that
the
exte
nd
edlif
eti
res
last
has
am
ean
11E
=70
and
stan
dard
devi
atio
na5
=7.
Ifm
ilea
ges
for
both
tire
s
follo
wa
norm
aldi
stri
buti
on,
wha
tis
the
prob
abil
ity
that
ara
ndom
lyse
lect
edst
anda
rdm
odel
tire
will
get
mor
em
ilea
geth
ana
rand
omly
sele
cted
exte
nd
edlif
eti
re?
(A)
0.10
8(B
)0.
123
(C)
0.43
4(D
)0.
566
(E)
0.59
2
7.W
hen
play
ing
the
card
gam
eB
lack
jack
,m
ulti
ple
deck
sar
eus
edan
dre
shuf
fled
ofte
nso
that
the
outc
omes
ofth
eca
rds
deal
tar
eap
prox
imat
ely
inde
pend
ent.
Whe
na
play
erre
ceiv
estw
oca
rds
that
are
aco
mbi
nati
onof
anac
ean
da
face
card
,th
isis
call
eda
“nat
ural
blac
kjac
k”an
dau
tom
atic
ally
win
s.A
natu
ral
blac
kjac
ksh
ould
occu
rin
4.5%
ofth
ero
unds
play
ed.
Wha
tis
the
prob
abil
ity
that
a
play
erpl
ays
20ro
unds
ofB
lack
jack
and
gets
two
orm
ore
natu
ral
blac
kjac
ks?
(A)
0.05
9(B
)0.
168
(C)
0.22
7(D
)0.
773
(E)
0.90
0
8.By
one
esti
mat
e,3%
ofal
lS
iber
ian
Hus
kypu
ppie
sar
ebo
rnw
ithtw
odi
ffer
ent
colo
red
eyes
(cal
led
hete
roch
rom
iair
idum
).Fo
rra
ndom
sam
ples
of50
Sib
eria
nH
usky
pupp
ies,
wha
tar
eth
em
ean
and
stan
dard
devi
atio
nof
the
num
ber
ofpu
ppie
sth
atw
illha
vetw
odi
ffer
ent
colo
red
eyes
?
(A)
p=
0.03
,a=
0.02
4(B
)p
=0.
03,a
=0.
171
(C)
p=
1.5,
a=
1.20
6(D
)p
=1.
5,a
=1.
455
(E)p
=3,a
=50
.
‘4’ST
ATS
MED
IC
4
9.U
sing
data
coll
ecte
dfr
om19
81to
2010
for
Ann
Arb
or,
MI
(GO
BLU
EI),
the
aver
age
“hig
h”
tem
per
atu
refo
rda
ysin
July
has
am
ean
of28
.9°
Cel
sius
with
ast
anda
rdde
viat
ion
of3.
3°C
elsi
us.
Wha
tar
eth
em
ean
and
stan
dard
devi
atio
nif
the
tem
pera
ture
sar
eco
nver
ted
todeg
rees
Fah
renh
eit?
(A)
Mea
nis
84.0
2°F
,S
tand
ard
devi
atio
nis
1.83
°F.
(B)
Mea
nis
52.0
2°F
,S
tand
ard
devi
atio
nis
5.94
°F.
(C)
Mea
nis
84.0
2°F
,S
tand
ard
devi
atio
nis
5.94
°F.
(D)
Mea
nis
84.0
2°F
,S
tand
ard
devi
atio
nis
35.2
8°F
.
(E)
Mea
nis
84.0
2°F
,S
tand
ard
devi
atio
nis
37.9
4°F
.
10.
The
scor
eson
the
verb
alse
ctio
nof
the
Gra
duat
eR
ecor
dsE
xam
inat
ion
(GR
E)ar
eap
prox
imat
ely
norm
ally
dist
ribu
ted
with
am
ean
of15
0an
da
stan
dard
devi
atio
nof
B.5
.W
hat
isth
epr
obab
ilit
yth
at
ara
ndom
lyse
lect
edsc
ore
onth
eve
rbal
sect
ion
ishi
gher
than
165?
(A)
0.01
8(B
)0.
039
(C)
0.96
1(D
)0.
982
(E)
Can
not
bede
term
ined
11.
The
fini
shin
gti
mes
ofa
5Kra
ceru
nby
com
peti
tive
mal
eru
nner
sag
e15
-18
are
appr
oxim
atel
y
norm
aldi
stri
buti
onw
itha
mea
nti
me
of18
min
utes
and
ast
anda
rdde
viat
ion
of2
min
utes
.A
part
icul
arly
toug
h5K
race
tend
sto
take
thes
esa
me
runn
ers
4.5
addi
tion
alm
inut
es.
To
earn
a
com
plet
ion
med
alin
this
part
icul
ar5K
race
,th
eru
nner
mus
tco
mpl
ete
the
race
with
in25
min
utes
.
App
roxi
mat
ely,
wha
tpe
rcen
tof
com
peti
tive
mal
eru
nner
sin
the
15-1
8ag
ebr
acke
tty
pica
llydo
not
earn
aco
mpl
etio
nm
edal
atth
isra
ce?
(A)
App
roxi
mat
ely
0%
(B)
10.5
6%
(C)
14.0
8%
(D)
28.
93%
(E)
35.0
3%
‘4’ST
ATS
MED
IC
...
.12
.A
poll
ster
aske
d10
0pe
ople
“If
mon
eyw
asno
ta
fact
or,
how
man
ych
ildr
enw
ould
you
like
to
have
?”T
here
sult
san
dth
eir
freq
uenc
ies
are
show
nin
the
(est
imat
ed)
prob
abil
ity
dist
ribu
tion
func
tion
tabl
ebe
low
.
X0
12
34
P<
)?
0.26
0.29
0.15
0.05
Wha
tis
the
prob
abil
ity
that
the
num
ber
ofch
ildr
ena
rand
omly
sele
cted
pers
onfr
omth
issa
mpl
e
wou
ldlik
eto
have
isle
ssth
anth
em
ean
ofX
?
(A)
0.25
(B)
0.49
(C)
0.51
(D)
0.80
(E)
1.49
., 15
.In
ala
rge
scho
oldi
stri
ct,
itis
know
nth
at25
%of
all
stud
ents
ente
ring
kind
erga
rten
are
alre
ady
read
ing.
Asi
mpl
era
ndom
sam
ple
of10
new
kind
erga
rten
ers
isdr
awn.
Wha
tis
the
prob
abil
ity
that
few
erth
anth
ree
ofth
emar
eab
leto
read
?
(A)
0.25
03
(B)
0.28
16
(C)
0.50
00
(D)
0.52
56
(E)
0.77
59
16.
Adi
cega
me
ata
loca
lca
rniv
alus
esa
10-s
ided
die
whi
chha
sbe
enri
gged
.T
heev
ennu
mbe
red
outc
omes
(2,
4,6,
8,an
d10
)ha
vebe
enm
ade
ligh
ter
soth
atth
eyar
eth
ree
tim
esm
ore
likel
yto
occu
ras
the
odd
num
bere
dou
tcom
es(1
,3,
5,7,
and
9).
Apl
ayer
that
rolls
anod
dnu
mbe
rw
ins
the
gam
e.W
hat
isth
epr
obab
ilit
yof
win
ning
this
gam
e?
13.
Em
ploy
ees
that
wor
kat
afi
shst
ore
mus
tm
easu
reth
ele
vel
ofni
trit
esin
the
wat
erea
chda
y.
Nitr
itele
vels
shou
ldre
mai
nlo
wer
than
5pp
mas
tono
tha
rmth
efi
sh.
The
nitr
ite
leve
lva
ries
acco
rdin
gto
adi
stri
buti
onth
atis
appr
oxim
atel
yno
rmal
with
am
ean
of3
ppm
.T
hepr
obab
ilit
yth
at
the
nitr
ite
leve
lis
less
than
2pp
mis
0.09
18.
Whi
chof
the
foll
owin
gis
clos
est
toth
epr
obab
ilit
yth
at
ona
rand
omly
sele
cted
day
the
nitr
ite
leve
lw
illbe
atle
ast
5pp
m?
(A)
0.05
(B)
0.15
(C)
0.20
(D)0
.25
(E)
0.50
(A)
0.00
39
(B)
0.02
66
(C)
0.09
18
(D)
0.75
19
(E)
0.99
61
14.
Acc
ordi
ngto
ast
udy,
91%
ofal
lad
ults
have
ace
llph
one.
An
empl
oyee
ofa
cell
phon
eco
mpa
ny
atte
nd
sa
com
mun
ity
even
tan
dha
sa
spec
ial
offe
rto
give
tofi
rst
tim
ece
llph
one
owne
rs.
Ifsh
e
rand
omly
sele
cts
adul
tsin
atte
ndan
ceat
the
even
tan
dce
llph
one
owne
rshi
pis
ind
epen
den
tfr
om
adul
tto
adul
t,w
hat
isth
epr
obab
ilit
yth
atsh
eas
ks20
adul
tsk
fQre
find
ing
one
that
do
esno
tow
na
cell
phon
e?
(A)
(0.9
1)20
(0.0
9)
(B)
(0.0
9)20
(0.9
1)
(C)
20(0
.91)
20(0
.09)
(D)
20(0
.09)
20(0
.91)
(E)
20(0
.09)
(0.9
1)
17.
Air
lines
mus
tbe
awar
eof
the
wei
ght
ofth
eai
rcra
ftpl
usev
eryt
hing
onbo
ard.
Bas
edon
thou
sand
sof
flig
hts,
the
mea
nan
dst
anda
rdde
viat
ion
for
the
wei
ghts
ofse
vera
lit
ems
are
show
nin
the
tabl
e.T
hew
eigh
tsof
the
airp
lane
,peo
ple
/luggag
e,an
dfu
elar
eas
sum
edto
bein
depe
nden
t.
Item
Mea
n(in
Sta
ndar
dD
evia
tion
(in
tons
)to
ns)
Pla
ne45
2
Peo
ple
/lu
gg
age
101
Fuel
201
Let
the
rand
omva
riab
leT
repr
esen
tth
eto
tal
wei
ght
ofth
epl
ane,
peo
ple
/luggag
e,an
dfu
elfo
ra
rand
omly
sele
cted
flig
ht.
Whi
chof
the
foll
owin
gis
clos
est
toth
est
anda
rdde
viat
ion
of7?
(A)
2.45
tons
(B)
4.00
tons
(C)
6.00
tons
(D)
75.0
tons
(E)
120
tons
4’ST
ATS
MED
IC4’
STAT
SM
EDIC
18.
Acc
ordi
ngto
the
Gui
nnes
sB
ook
ofW
orld
Rec
ords
,a
wom
anfr
omR
ussi
a,M
rs.
Vas
sily
eva,
had
69ch
ildr
enbe
twee
nth
eye
ars
1725
to17
65.
She
had
16pa
irs
oftw
ins,
7se
tsof
trip
lets
,an
d4
sets
ofqu
adru
plet
s.S
uppo
seon
eof
the
birt
hsis
rand
omly
sele
cted
.G
iven
that
Mrs
.V
assi
lyev
aga
ve
birt
hto
atle
ast
3ch
ildr
en(t
ripl
ets)
,w
hat
isth
epr
obab
ilit
yth
atsh
ega
vebi
rth
toqu
adru
plet
s?
(A)
4/27
(B)
7/11
(C)
3/11
(D)
3/27
(E)
4/11
20.
Bas
edon
stu
den
tre
cord
s,25
%of
the
stud
ents
ata
larg
ehi
ghsc
hool
have
aG
PAof
3.5
or
bett
er,
16%
ofth
est
uden
tsar
ecu
rren
tly
enro
lled
inat
leas
ton
eA
Pcl
ass,
and
12%
ofth
est
uden
ts
have
aG
PAof
3.5
orbet
ter
and
are
enro
lled
inat
leas
ton
eA
Pcl
ass.
Ifw
ese
lect
one
stud
ent
at
rand
om,
wha
tis
the
prob
abil
ity
that
the
stu
den
tha
sa
GPA
low
erth
an3.
5an
dis
not
taki
ngan
yA
P
clas
ses?
(A)
0.29
(B)
0.47
(C)
0.53
(D)
0.63
(E)
0.71
19.
Apa
rtic
ular
man
ufac
ture
rof
refr
iger
ator
sha
sco
me
unde
rfi
reas
thei
r$1
,700
LGA
mod
elha
s
fail
edfo
rasi
gnif
ican
tpo
rtio
nof
owne
rs.
The
LGA
mod
elof
ten
fail
edap
prox
imat
ely
1-2
year
saf
ter
purc
hase
,w
hich
isou
tsid
eth
ew
arra
nty
peri
od.
Acl
ass
acti
onla
wsu
itw
asfi
led
byow
ners
ofth
eLG
A
mod
elcl
aim
ing
that
the
man
ufac
ture
rsh
ould
repa
iror
repl
ace
the
units
.T
hela
wye
rre
pres
enti
ngth
e
clas
sac
tion
law
suit
obta
ined
alis
tof
LGA
owne
rsw
hoco
mpl
eted
regi
stra
tion
card
san
das
ked
a
sim
ple
rand
omsa
mpl
eof
1000
LGA
owne
rs,
“Is
your
LGA
refr
iger
ator
still
wor
king
?”H
eal
so
reco
rded
the
age
ofth
ere
frig
erat
orfr
omin
form
atio
npr
ovid
edon
the
regi
stra
tion
card
.H
ere
are
the
data
:
Aqe
ofth
eLG
AR
efri
qera
tor
Les
sth
an1
ito
2ye
ars
year
204
55
5116
5
Tot
alI
255
220
Mor
eth
an2
Tot
alye
ars
Wha
tis
the
prob
abil
ity
ara
ndom
lyse
lect
edLG
Are
frig
erat
oris
atle
ast
one
year
old
and
nolo
nger
wor
ks?
(A)
0.05
1(B
)0
13
5
(C)
0.48
0
(D)
0.53
1
(E)
0.90
4
.
+ST
ATS
MED
IC
.
‘I’ST
ATS
MED
IC
.,.
Iy5
Wor
king
?I I
No
210
I46
9I
315
I53
1I
525
I10
00I
Hnit 4 Practice Free Response Question
The Big River Casino is advertising a new digital lottery-style game called Instant Lotto. The playercan win the following monetary prizes with the associated probabilities:
• 5% probability to win $10• 4% probability to win $15• 3% probability to win $30• 1% probability to win $50• 0.1% probability to win the Grand Prize, $1000.
(a) Calculate the expected value of the prize for one play of Instant Lotto.
(b) As a promotion, a visitor to the casino is given 20 free plays of Instant Lotto. What is theprobability that the visitor wins some prize at least twice in the 20 free plays?
(c) The number of people who play Instant Lotto each day is approximately normally distributed witha mean of 800 people and a standard deviation of 310 people. What is the probability that arandomly selected day has at least 1000 people play Instant Lotto?
+ STATS MEDIC
11!
Unit 5 Free Response 2010 #2
2. A local radio station plays 40 rock-and-roll songs during each 4-hour show. The program director at the stationneeds to know the total amount of airtime for the 40 songs so that time can also be programmed during the showfor news and advertisements. The distribution of the lengths of rock-and-roll songs, in minutes, is roughlysymmetric with a mean length of 3.9 minutes and a standard deviation of 1.1 minutes.
(a) Describe the sampling distribution of the sample mean song lengths for random samples of 40 rock-and-rollsongs.
(b) If the program manager schedules 80 minutes of news and advertisements for the 4-hour (240-minute) show,only 160 minutes are available for music. Approximately what is the probability that the total amount oftime needed to play 40 randomly selected rock-and-roll songs exceeds the available airtime?
Source: Copyright © The College Board.*AP is a registered trademark of the College Board which was not irwolved in the production of,
and does not endorse, this product.
Unit
5M
ult
iple
Choic
e
1.In
ala
rge
city
,46
%of
adul
tssu
ppor
tth
elo
cal
foot
ball
team
buil
ding
ane
wst
adiu
m.
Ifa
poll
is
take
nfr
oma
rand
omsa
mpl
eof
80ad
ults
inth
ela
rge
city
,w
hich
ofth
efo
llow
ing
prop
erly
desc
ribe
s
the
sam
plin
gdi
stri
buti
onof
the
sam
ple
prop
orti
onof
adul
tsw
hosu
ppor
tth
est
adiu
m?
(A)
=36
.8,r
4.46
,th
edi
stri
buti
onis
appr
oxim
atel
yno
rmal
.
(B)j
=36
.8,a
4.46
,sh
ape
ofth
edi
stri
buti
onis
unkn
own.
(C)
=0.
46,o
=0.
056,
the
dist
ribu
tion
isap
prox
imat
ely
norm
al.
(D)p
=0.
46,u
=0.
056,
shap
eof
the
dist
ribu
tion
isun
know
n.
(E)
=43
.2,u
4.46
,th
edi
stri
buti
onis
bino
mia
l.
2.W
hich
ofth
efo
llow
ing
stat
emen
tsis
true
?
(A)
Apa
ram
eter
isa
num
ber
that
desc
ribe
sso
me
char
acte
rist
icof
asa
mpl
e.
(B)
An
unbi
ased
esti
mat
oris
any
stat
isti
cth
atis
take
nfr
oma
sam
ple
chos
enby
rand
omm
etho
ds.
(C)
Asa
mpl
ing
dist
ribu
tion
isth
edi
stri
buti
onof
ast
atis
tic
calc
ulat
edfr
omal
lpo
ssib
lesa
mpl
esof
the
sam
esi
zefr
omth
esa
me
popu
lati
on.
(D)
The
vari
abili
tyof
apo
pula
tion
dist
ribu
tion
will
dec
reas
eas
the
sam
ple
size
incr
ease
s.
(E)
Ano
rmal
appr
oxim
atio
nca
nal
way
sbe
used
for
the
sam
plin
gdi
stri
buti
onof
aslo
ngas
the
sam
ple
size
isgre
ater
than
30.
3.T
hew
eigh
tof
asi
ngle
bag
chec
ked
byan
airp
lane
pas
senger
follo
ws
adi
stri
buti
onth
atis
righ
t
skew
edw
itha
mea
nof
38po
unds
and
ast
anda
rdde
viat
ion
of6.
2po
unds
.If
ara
ndom
sam
ple
of96
bags
isse
lect
ed,
wha
tis
the
prob
abil
ity
that
the
aver
age
wei
ght
ofth
eba
gsex
ceed
s40
poun
ds?
(A)
0.00
08(B
)0.
0011
(C)
0.37
35(D
)0.
9992
(E)
Itis
not
appr
opri
ate
tous
ea
norm
aldi
stri
buti
onto
calc
ulat
epr
obab
ilit
yin
this
situ
atio
n.
.,...
4.B
elow
are
hist
ogra
ms
disp
layi
ngth
eva
lues
take
nby
thre
esa
mpl
est
atis
tics
inse
vera
lhu
ndre
d
sam
ples
from
the
sam
epo
pula
tion
.E
ach
hist
ogra
mha
sth
esa
me
scal
ean
dth
etr
ueva
lue
ofth
e
popu
lati
onpa
ram
eter
ism
arke
dby
anar
row
onea
chhi
stog
ram
.W
hich
stat
isti
cis
the
best
esti
mat
or
ofth
epa
ram
eter
?
AB
C
II
(A)
Sta
tist
icA
beca
use
Aan
dB
are
unbi
ased
but
Aha
shi
gher
vari
abili
ty.
(B)
Sta
tist
icB
beca
use
Aan
dB
are
unbi
ased
but
Bha
slo
wer
vari
abili
ty.
(C)
Sta
tist
icC
beca
use
itis
alw
ays
bet
ter
toun
dere
stim
ate
rath
erth
anov
eres
tim
ate.
(D)
Sta
tist
ics
Aor
Bbe
caus
eth
epo
pula
tion
para
met
eris
inth
ece
nter
ofth
esa
mpl
ing
dist
ribu
tion
s
for
both
.(E
)S
tati
stic
sA
,B
orC
beca
use
all
cont
ain
the
popu
lati
onpa
ram
eter
inth
esa
mpl
ing
dist
ribu
tion
s.
5.A
com
pany
inte
nds
toco
llec
ta
rand
omsa
mpl
eof
size
nfr
oma
popu
lati
onw
ithpo
pula
tion
prop
orti
onof
inte
rest
p.W
hich
ofth
efo
llow
ing
situ
atio
nsw
ould
resu
ltin
the
smal
lest
stan
dard
devi
atio
nof
the
sam
plin
gdi
stri
buti
onof
i3?
(A)
The
popu
lati
onpr
opor
tion
p0.
5,an
dth
esa
mpl
esi
zeis
n.
(B)
The
popu
lati
onpr
opor
tion
p*
0.5,
and
the
sam
ple
size
isn.
(C)
The
popu
lati
onpr
opor
tion
p0.
5,an
dth
esa
mpl
esi
zeis
2n.
(D)
The
popu
lati
onpr
opor
tion
p*
0.5,
and
the
sam
ple
size
is2n
.
(E)
The
reis
not
enou
ghin
form
atio
npr
ovid
edto
dete
rmin
eth
esm
alle
stst
anda
rdde
viat
ion
ofth
e
sam
plin
gdi
stri
buti
on.
.,..........
..
iIIii
1IIIii1 I
+ST
ATS
MED
ICif
STAT
SM
EDIC
6.K
ent
coun
tyan
dO
akla
ndco
unty
are
loca
ted
onth
ew
est
and
east
side
sof
Mic
higa
n,re
spec
tive
ly.
Info
rmat
ion
abo
ut
the
year
lyho
useh
old
inco
me
isgi
ven
inth
eta
ble
belo
w.
Bot
hdi
stri
buti
ons
are
stro
ngly
skew
edri
ght.
Ara
ndom
sam
ple
of10
0ho
useh
olds
ista
ken
from
each
ofth
eve
ryla
rge
popu
lati
ons.
Whi
chof
the
follo
win
gde
scri
bes
the
sam
plin
gdi
stri
buti
onof
the
diff
eren
cein
sam
ple
mea
ns?
nM
ean
(dol
lars
)S
td.
Dev
.(d
olla
rs)
Oak
land
Cou
nty
100
66,4
0048
,400
Ken
tC
ount
y10
054
,340
39700
(A)
=12
060,
=87
0,th
edi
stri
buti
onis
appr
oxim
atel
yno
rmal
(B)
=12
060,
=62
59.9
1,th
edi
stri
buti
onis
stro
ngly
skew
edri
ght
(C)
tiO
jK=
1206
0,0O
-2K
=62
59.9
1,th
edi
stri
buti
onis
appr
oxim
atel
yno
rmal
(D)
=12
060,
OK
=88
10,
the
dist
ribu
tion
isst
rong
lysk
ewed
righ
t(E
)i1
1O
1K
=12
060,u_
=88
10,t
hedi
stri
buti
onis
appr
oxim
atel
yno
rmal
7.A
rece
ntre
port
stat
esth
at89
%of
Am
eric
ans
cons
ider
them
selv
esab
ove
aver
age
driv
ers.
Alo
cal
new
spap
eris
plan
ning
onco
nduc
ting
asu
rvey
toin
vest
igat
ew
heth
erth
isis
true
loca
lly.
Ifth
ene
wsp
aper
assu
mes
that
the
89%
clai
mis
true
and
plan
sto
use
the
norm
alap
prox
imat
ion
toca
lcul
ate
prob
abil
itie
sas
soci
ated
with
thei
rsa
mpl
epr
opor
tion
,w
hich
sam
ple
size
wou
ldbe
mos
tap
prop
riat
e?(A
)10
(B)
11
(C)
30(D
)91
(F)
The
num
ber
dep
ends
onth
esi
zeof
the
popu
lati
on.
8.D
aren
and
Josh
are
pret
tygo
odfr
eeth
row
shoo
ters
.D
aren
mak
es75
%of
the
free
thro
ws
heat
tem
pts.
Josh
mak
es80
%of
his
free
thro
ws.
Sup
pose
we
take
sep
arat
era
ndom
sam
ples
of50
free
thro
ws
each
from
Dar
enan
dJo
sh,
and
reco
rdth
epr
opor
tion
offr
eeth
row
sth
atar
em
ade
byea
ch.
Whi
chof
the
follo
win
gbe
stde
scri
bes
the
sam
plin
gdi
stri
buti
onof
(A)
Str
ong
skew
,w
ithm
ean
-0.0
5an
dst
anda
rdde
viat
ion
0.08
3(B
)A
ppro
xim
atel
yno
rmal
,w
ithm
ean
-0.0
5an
dst
anda
rdde
viat
ion
0.08
3(C
)S
hape
cann
otbe
dete
rmin
ed,
with
mea
nof
-0.0
5an
dst
anda
rdde
viat
ion
0.08
3(D
)S
tron
gsk
ew,
with
mea
n-0
.05
and
stan
dard
devi
atio
n0.
118
(E)
App
roxi
mat
ely
norm
al,
with
mea
n-0
.05
and
stan
dard
devi
atio
n0.
118
9.D
onne
rS
umm
it,
Cal
ifor
nia,
isa
popu
lar
ski
reso
rtar
ea.
Ove
rth
epa
st60
year
s,th
ean
nual
snow
fall
tota
lsof
Don
ner
Sum
mit
have
foll
owed
adi
stri
buti
onth
atis
stro
ngly
skew
edri
ght
with
am
ean
of40
4in
ches
and
ast
anda
rdde
viat
ion
of12
9in
ches
.If
man
ysa
mpl
esof
size
9w
ere
take
n,w
hich
ofth
efo
llow
ing
wou
ldbe
stde
scri
beth
esh
ape
ofth
esa
mpl
ing
dist
ribu
tion
oft?
(A)
The
shap
eis
appr
oxim
atel
yno
rmal
sinc
eth
esa
mpl
esi
zeis
reas
onab
lyla
rge.
(B)
The
shap
eis
skew
edri
ght
sinc
enp
10an
dn(1
—p)
10ha
veno
tbe
enm
et.
(C)
The
shap
eis
equa
lly
assk
ewed
righ
tas
the
popu
lati
ondi
stri
buti
on.
(D)
The
shap
eis
skew
edri
ght
but
less
soth
anth
epo
pula
tion
dist
ribu
tion
.
(E)
Can
not
bede
term
ined
from
the
give
nin
form
atio
n.
10.
The
heig
hts
ofal
lad
ult
mal
esin
Cro
atia
are
appr
oxim
atel
yno
rmal
lydi
stri
bute
dw
itha
mea
nof
180c
man
da
stan
dard
devi
atio
nof
7cm
.T
hehe
ight
sof
all
adul
tfe
mal
esin
Cro
atia
are
appr
oxim
atel
yno
rmal
lydi
stri
bute
dw
itha
mea
nof
158
cman
da
stan
dard
devi
atio
nof
9cm
.If
ind
epen
den
tra
ndom
sam
ples
of10
adul
tm
ales
and
10ad
ult
fem
ales
are
take
n,w
hat
isth
epr
obab
ilit
yth
atth
edi
ffer
ence
insa
mpl
em
eans
(mal
es—
fem
ales
)is
gre
ater
than
20cm
?
(A)
0.34
63
(B)
0.65
37
(C)
0.68
27
(D)
0.71
04
(E)
0.86
87
.
+ST
ATS
MED
IC
0
+ST
ATS
MED
IC
•*
nit 5 Practice Free Response Question
A regulation baseball can weigh no more than 149 grams. A factory produces baseballs with weightsthat are normally distributed with a mean of 146 grams and a standard deviation of 2.3 grams.
(a) If a baseball produced by the factory is randomly selected, what is the probability that it is withinregulation weight?
(b) The baseballs are shipped in boxes of 16. What is the probability that at least 15 of the 16baseballs in a pack are within regulation weight?
(c) The factory will not ship a box of 16 if the average weight of the baseballs in the box exceeds 147grams. What is the probability that a pack of 16 baseballs would have an average weight of morethan 147 grams?
+ STATS MEDIC
..:
Unit 6 Free Response 2017 #2
2. The manager of a local fast-food restaurant is concerned about customers who ask for a water cup when placingan order but fill the cup with a soft drink from the beverage fountain instead of filling the cup with water. Themanager selected a random sample of 80 customers who asked for a water cup when placing an order and foundthat 23 of those customers filled the cup with a soft drink from the beverage fountain.
(a) Construct and interpret a 95 percent confidence interval for the proportion of all customers who, havingasked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain.
(b) The manager estimates that each customer who asks for a water cup but fills it with a soft drink costs therestaurant $0.25. Suppose that in the month of June 3,000 customers ask for a water cup when placingan order. Use the confidence interval constructed in part (a) to give an interval estimate for the cost tothe restaurant for the month of June from the customers who ask for a water cup but fill the cup witha soft drink.
Source: Copyright © The College Board.*AP is a registered trademark of the College Board, which was not involved in the production of,
and does not endorse, this product.
Uni
t6
Mul
tipl
eC
hoic
e
1.A
nA
PS
tati
stic
scl
ass
surv
eys
24ra
ndom
lyse
lect
edfe
mal
est
uden
tsfr
omth
eir
high
scho
ol,
and
calc
ulat
esa
95%
conf
iden
cein
terv
alfo
rth
em
ean
heig
htof
fem
ale
stud
ents
tobe
63.4
±1.
6in
ches
.
Whi
chof
the
foll
owin
gis
aco
rrec
tin
terp
reta
tion
ofth
isin
terv
al?
(A)
The
reis
a95
%pr
obab
ilit
yth
atth
etr
uem
ean
heig
htof
fem
ale
stud
ents
atth
esc
hool
falls
betw
een
61.8
and
65.0
inch
es.
(B)
We
can
be95
%co
nfid
ent
that
the
true
mea
nhe
ight
offe
mal
est
uden
tsat
the
scho
olis
63.4
inch
es.
(C)
95%
ofth
eti
me,
we
can
beco
nfid
ent
that
the
mea
nsa
mpl
ehe
ight
offe
mal
est
uden
tsw
illfa
ll
betw
een
61.8
and
65.0
inch
es.
(D)
We
can
be
95%
conf
iden
tth
atth
etr
uem
ean
heig
htof
fem
ale
stud
ents
atth
esc
hool
isbe
twee
n
61.8
and
65.0
inch
es.
(E)
The
reis
a95
%pr
obab
ilit
yth
atth
etr
uem
ean
heig
htof
fem
ale
stud
ents
atth
esc
hool
is63
.4
inch
es.
2.A
rand
omsa
mpl
eof
18ad
ults
,ch
osen
from
the
1500
adul
tsin
the
tow
n,to
oka
surv
eyas
king
thei
r
opin
ion
ona
rece
ntpr
oper
tyta
xch
ange
.25
%of
thos
ew
hore
sponded
said
they
wer
ein
favo
rof
the
chan
ge.
The
com
pany
runn
ing
the
surv
eyw
ants
toco
nstr
uct
aco
nfid
ence
inte
rval
esti
mat
ing
the
prop
orti
onof
all
adul
tsin
the
tow
nw
hosu
ppor
tth
ech
ange
.W
hich
ofth
eco
ndit
ions
for
infe
renc
e
have
been
sati
sfie
d?
I.R
ando
mco
ndit
ion
II.N
orm
alco
ndit
ion
III.
10%
cond
itio
n
(B)
II
(C)
Iand
Ill(D
)II
and
Ill(E
)I,
II,an
dIll
3.Fo
rw
hich
ofth
efo
llow
ing
sam
ples
wou
ldit
beap
prop
riat
eto
use
t-pr
oced
ures
for
infe
renc
efo
r
the
popu
lati
onm
ean?
(A)
Ill(B
)Ia
ndII
(C)
Iand
III
(D)
IIan
dIll
(E)
I,II,
and
III
I—1_fl
_II
II_sI
II
4.T
hest
uden
tsof
aS
tati
stic
scl
ass
wan
tto
esti
mat
eho
wm
any
year
sit
take
sfo
ra
univ
ersi
ty
prof
esso
rto
earn
aPh
D.
The
ysu
rvey
ara
ndom
sam
ple
of40
prof
esso
rsw
ithPh
Ds,
whi
chre
sult
sin
a
sam
ple
mea
nof
5.4
year
san
da
stan
dard
devi
atio
nof
1.6
year
s.W
hich
ofth
efo
llow
ing
repr
esen
ts
the
95%
conf
iden
cein
terv
alfo
rth
etr
uem
ean
ofth
enu
mbe
rof
year
sit
take
sa
prof
esso
rto
earn
a
PhD
?
(A)
5.4
±1.
96(1
.6)
(B)
5.4
±1.
9616
40
(C)
5.4
±1
.96
--
(D)
5.4
+2.O
9-
—40
(E)
5.4
±2.O
9--
5.A
stud
yin
tend
sto
esti
mat
ea
popu
lati
onm
ean
with
anun
know
npo
pula
tion
stan
dard
devi
atio
n
and
asa
mpl
esi
zeof
15.
Whi
chof
the
foll
owin
gis
clos
est
toth
eap
prop
riat
ecr
itica
lva
lue
tocr
eate
a
98%
conf
iden
cein
terv
al?
(A)
2.05
5(B
)2.
249
(C)
2.26
4(D
)2.
602
(E)
2.62
4
...
n=12
n=19
n=31
+ST
ATS
MED
IC+
STAT
SM
EDIC
6.A
new
spap
erpl
ans
toco
nduc
ta
surv
eyfo
rth
eup
com
ing
pres
iden
tial
elec
tion
inor
der
toes
tim
ate
the
prop
orti
onof
the
popu
lati
on,
p.w
hosu
ppor
tsa
cert
ain
cand
idat
e.W
hat
isth
esm
alle
stsa
mpl
esi
zenee
ded
toob
tain
anes
tim
ate
that
isw
ithin
4%of
the
true
prop
orti
onpat
the
96%
conf
iden
cele
vel?
(A)
26(B
)37
6(C
)60
1(D
)66
0(E
)C
anno
tbe
dete
rmin
edfr
omin
form
atio
ngi
ven.
7.A
rand
omsa
mpl
eof
size
nis
coll
ecte
dfr
oma
cons
ider
ably
larg
erpo
pula
tion
ofsi
zeN
.T
hat
sam
ple
isus
edto
crea
tea
95%
conf
iden
cein
terv
alto
esti
mat
ea
popu
lati
onpr
opor
tion
.U
sing
the
sam
esa
mpl
epr
opor
tion
,th
eco
nfid
ence
inte
rval
wou
ldbe
narr
ower
if:
(A)
Asm
alle
rsa
mpl
esi
zew
asus
ed.
(B)
At-
proc
edur
ew
asus
edin
stea
dof
az-
proc
edur
e.(C
)A
high
erco
nfid
ence
leve
lw
asus
ed.
(D)
The
popu
lati
onsi
zeN
was
larg
er.
(E)
Alo
wer
conf
iden
cele
vel
was
used
.
8.E
lect
ric
vehi
cles
mak
eup
ave
rysm
all
prop
orti
onof
the
over
all
car
mar
ket,
but
byho
wm
uch
has
that
prop
orti
onin
crea
sed?
Ind
epen
den
tsu
rvey
sof
rand
omly
sele
cted
car
deal
ersh
ips
wer
eco
mpl
eted
,w
ith0.
1%of
the
10,0
00ca
rsso
ldin
the
2012
sam
ple
bein
gel
ectr
icve
hicl
es,
and
0.5%
perc
ent
ofth
e20
,000
cars
inth
e20
16sa
mpl
ebe
ing
elec
tric
vehi
cles
.W
hich
ofth
efo
llow
ing
repr
esen
tsa
95%
conf
iden
cein
terv
alfo
rth
ech
ange
inth
epr
opor
tion
ofel
ectr
icca
rsso
ldfr
om20
12to
2016
?
(A)
(0.0
05—
0.00
1)±
1.96
/o.o
os_o
.oos
)+
0.0
01
(1-0
.00
1)
20
.00
01
0.0
00
(B)
(0.0
05—
0.00
1)±
1.65
/0.0
01(1
-0.0
05)
+0
.00
1(1
-0.0
01
)
‘q2
0,0
00
10
,00
0
(C)
(0.0
05—
0.00
1)±
1.96
/o.o
o37u
_o.0
o37)
+0
.00
37
(1—
0.0
03
7)
42
0,0
00
10
,00
0
(D)
(0.0
04)
+1.
96/0
00
4(1
_0
00
4)
—
30
.00
0
(E)
(0.0
037)
±1.
96/0
.0037(1
-0.0
037)
‘,43
0,0
00
9.A
rece
ntst
udy
exam
inin
gth
eef
fect
sof
suga
rco
nsum
ptio
non
am
iddl
esc
hool
stud
ent’
sab
ility
tofo
cus
ona
read
ing
assi
gnm
ent
used
18vo
lunt
eer
subj
ects
and
divi
ded
them
into
9pa
irs
base
don
thei
rre
adin
gsp
eeds
.O
nera
ndom
lyas
sign
edm
embe
rof
each
pair
was
give
na
beve
rage
cont
aini
nga
subs
tant
ial
amou
ntof
suga
r,an
dth
eot
her
dran
ka
suga
r-fr
eeve
rsio
nof
the
beve
rage
.E
ach
subj
ectw
asgi
ven
apa
ssag
eto
read
and
the
tim
e(in
seco
nds)
itto
okto
read
was
reco
rded
.T
hedi
ffer
ence
for
each
pair
isca
lcul
ated
(sug
ar—
suga
r-fr
ee).
A90
%co
nfid
ence
inte
rval
for
the
mea
ndi
ffer
ence
inre
adin
gti
mes
is(-
5.8,
0.15
).
(A)
Bec
ause
the
cent
erof
the
inte
rval
is-2
.825
,w
eha
veco
nvin
cing
evid
ence
that
suga
rca
uses
fast
er
read
ing
tim
es,
onav
erag
e.(B
)B
ecau
seth
eco
nfid
ence
inte
rval
incl
udes
0,w
edo
n’t
have
conv
inci
ngev
iden
ceth
atsu
gar
caus
esfa
ster
read
ing
tim
es,
onav
erag
e.(C
)B
ecau
seth
eco
nfid
ence
inte
rval
incl
udes
0,w
eha
veco
nvin
cing
evid
ence
that
suga
rca
uses
fast
er
read
ing
tim
es,
onav
erag
e.(D
)B
ecau
seth
eco
nfid
ence
inte
rval
incl
udes
mor
ene
gati
veth
anpo
siti
veva
lues
,w
eha
veco
nvin
cing
evid
ence
that
suga
rca
uses
fast
erre
adin
gti
mes
,on
aver
age.
(E)
Cau
sati
onsh
ould
not
bein
ferr
edbe
caus
eth
esu
bjec
tsw
ere
volu
ntee
rs.
10.
Aso
cial
med
iade
velo
per
wan
tsto
dete
rmin
eif
the
prop
orti
onof
teen
ager
sw
hous
eF
aceb
ook
isth
esa
me
asth
epr
opor
tion
ofte
enag
ers
who
use
Sna
pcha
t.S
heta
kes
ara
ndom
sam
ple
of10
0te
enag
ers
and
find
sth
at75
ofth
e10
0st
uden
tsus
eF
aceb
ook
and
89of
the
100
stud
ents
use
Sna
pcha
t.W
ould
itbe
reas
onab
lefo
rth
eso
cial
med
iade
velo
per
toco
nstr
uct
a95
%co
nfid
ence
inte
rval
for
the
true
diff
eren
cein
prop
orti
onof
teen
ager
sth
atus
eF
aceb
ook
and
Sna
pcha
t?
(A)
No,
the
rand
omco
ndit
ion
isno
tsa
tisf
ied.
(B)
No,
the
norm
alco
ndit
ion
isno
tsa
tisf
ied.
(C)
No,
the
two
sam
ples
are
not
inde
pend
ent.
(D)
Yes
,al
lco
ndit
ions
have
been
met
.(E
)C
anno
tbe
dete
rmin
edfr
omth
egi
ven
info
rmat
ion.
.
‘4’ST
ATS
MED
IC4’
STAT
SM
EDIC
.,,
‘1
2
+
i, ii
g g a
‘St
2
+
,.40 4
15.
As
the
tem
per
atu
reri
ses
inC
hica
go,
does
the
crim
era
teal
sori
se?
Usi
ngda
taav
aila
ble
from
the
Chi
cago
Polic
eD
epar
tmen
t,an
inte
rest
edci
tizen
reco
rded
the
high
tem
per
atu
rean
dnu
mbe
rof
crim
esre
port
edfo
r8
rand
omly
sele
cted
days
.
Tem
pera
ture
°F17
3546
5564
7884
89
Num
ber
ofC
rim
es56
6066
7071
7874
76
The
citiz
enw
ants
tofi
nda
conf
iden
cein
terv
alth
atca
nbe
used
toes
tim
ate
the
num
ber
ofad
diti
onal
crim
esth
atca
nbe
exp
ecte
dto
bere
port
edfo
rea
chdeg
ree
that
the
daily
high
tem
per
atu
re
incr
ease
sw
ith95
%co
nfid
ence
.W
hich
ofth
efo
llow
ing
isth
em
ost
appr
opri
ate
proc
edur
efo
rsu
chan
inve
stig
atio
n?
(A)
Ach
i-sq
uare
test
ofas
soci
atio
n
(B)
Ali
near
regr
essi
ont-
inte
rval
for
slop
e
(C)
Aon
e-sa
mpl
et-
inte
rval
for
am
ean
(D)
Atw
o-sa
mpl
et-
inte
rval
for
adi
ffer
ence
ofm
eans
(E)
Aon
e-sa
mpl
ez-
inte
rval
for
apr
opor
tion
16.
Ala
rge-
sam
ple
95pe
rcen
tco
nfid
ence
inte
rval
for
the
prop
orti
onof
cred
itca
rdcu
stom
ers
that
have
repo
rted
frau
dule
ntch
arge
son
thei
rac
coun
tis
(0.0
28,
0.08
6).
Wha
tis
the
poin
tes
tim
ate
for
the
prop
orti
onof
all
cred
itca
rdcu
stom
ers
that
have
repo
rted
frau
dule
ntch
arge
son
thei
rac
coun
t?
(A)
0.05
7
(B)
0.05
8
(C)
0.02
9
(D)0
.114
(E)
0.19
6
.
‘4.ST
ATS
MED
IC
.
17.
Aw
rite
rfo
ra
care
erm
agaz
ine
isw
orki
ngon
anar
ticl
eab
out
the
proj
ecte
dca
reer
earn
ings
for
coll
ege
grad
uate
sin
vari
ous
fiel
ds.
He
sele
cts
ara
ndom
sam
ple
of25
educ
ator
san
dsu
rvey
sth
em
abo
ut
thei
rcu
rren
tsa
lary
,th
enu
mbe
rof
year
sth
eyha
vew
orke
din
the
fiel
d,an
dth
eir
pay
rais
e
stru
ctur
e.B
ased
upon
this
info
rmat
ion
heco
mpu
tes
the
aver
age
proj
ecte
dca
reer
earn
ings
for
grad
uate
sw
ithdeg
rees
ined
ucat
ion
tobe
$2.5
mill
ion
doll
ars
with
ast
anda
rdde
viat
ion
of0.
4
mill
ion
doll
ars.
Ass
umin
gal
lco
ndit
ions
for
infe
renc
ear
em
et,
whi
chof
the
foll
owin
gis
a90
perc
ent
conf
iden
cein
terv
alfo
rth
em
ean
proj
ecte
dca
reer
earn
ings
for
grad
uate
sw
ithdeg
rees
Ined
ucat
ion?
‘A’
25
+17
110.
4
(B)
2.5
±1.
645(
0.04
)
‘C’
25
+1
960
0.4
‘I.-.
‘D’
25
+1
645
0.4
‘I.-.
(B)
2.5
±1.
960(
0.04
)
18.
Are
cent
arti
cle
clai
med
that
wom
enar
ew
aiti
nglo
nger
toha
veth
eir
firs
tch
ild.
The
arti
cle
esti
mat
esth
atth
eav
erag
eag
eof
firs
t-ti
me
mot
hers
is26
year
sol
d,w
hich
isup
from
21ye
ars
old
in
1970
.T
hem
argi
nof
erro
rfo
rth
ees
tim
ate
was
1.5
year
s.B
ased
onth
ees
tim
ate
and
the
mar
gin
of
erro
r,w
hich
ofth
efo
llow
ing
isan
appr
opri
ate
conc
lusi
on?
(A)
95%
ofth
ew
omen
inth
est
udy
wer
e26
year
sol
dw
hen
they
had
thei
rfi
rst
child
.
(B)
The
age
ofev
ery
firs
t-ti
me
mot
her
inth
esa
mpl
em
ust
have
been
betw
een
24.5
and
27.5
year
s
old.
(C)
The
age
ofev
ery
firs
t-ti
me
mot
her
inth
esa
mpl
em
ust
have
been
betw
een
23an
d29
year
sol
d.
(D)
Thi
sst
udy
prov
esth
atw
omen
are
wai
ting
long
erto
have
thei
rfi
rst
child
.
(E)
Itis
plau
sibl
eth
atth
eav
erag
eag
eof
firs
t-ti
me
mot
hers
is27
year
sol
d.
+ST
ATS
MED
IC
•*
..
.19
.Ja
mes
has
ade
skjo
ban
dw
ould
like
tobe
com
em
ore
fit,
sohe
purc
hase
sa
trea
dw
alke
ran
da
stan
ding
desk
whi
chw
illal
low
him
tow
alk
ata
slow
pace
ashe
wor
ks.
How
ever
,he
isco
ncer
ned
that
stan
ding
and
wal
king
whi
lew
orki
ngm
ayca
use
his
prod
ucti
vity
tode
clin
e.A
fter
wor
king
this
way
for
6m
onth
she
take
sa
sim
ple
rand
omsa
mpl
eof
15da
ys.
He
reco
rds
how
long
hew
alke
dth
atda
y(in
hour
s)as
reco
rded
byhi
sfi
tnes
sw
atch
asw
ell
ashi
sbi
llab
leho
urs
for
that
day
asre
cord
edby
aw
ork
app
onhi
sco
mpu
ter.
Reg
ress
ion
Ana
lysi
s:B
illab
leho
urs
vers
usW
alk
tim
e
Pre
dic
tor
Co
efSE
Co
efT
PC
on
stan
t7.7
85
0.5
42
14
.36
30.0
00
Wal
kti
me
—0.
245
0.2
05
—1.
195
0.1
27
Ass
umin
gth
atal
lco
ndit
ions
for
infe
renc
ear
em
et,
whi
chof
the
foll
owin
gis
a95
perc
ent
conf
iden
ce
inte
rval
for
the
aver
age
chan
gein
the
num
ber
ofbi
llab
leho
urs
for
each
incr
ease
of1
hour
spen
t
wal
king
?(A
)—
0.24
5±
1.96
0(0.
205)
(B)
—0.
245
±2.
131(
0.20
5)
(C)
—0.
245
±2.
160(
0.20
5)
(D)
7.7
85±
1.96
0(0.
542)
(E)
7.78
5±
2.16
0(0.
542)
20.
Acu
riou
sst
uden
tw
ante
dto
dete
rmin
eif
ther
ew
asa
diff
eren
cein
the
aver
age
pric
eof
aqu
arte
r
poun
dha
mbu
rger
inth
eU
nite
dS
tate
san
dJa
pan.
The
studen
tra
ndom
lyse
lect
ed15
McD
onal
d’s
rest
aura
nts
inth
eU
nite
dS
tate
san
d10
McD
onal
d’s
rest
aura
nts
inJa
pan
and
reco
rded
the
pric
esof
thei
rqu
arte
rpo
und
ham
burg
ers.
Pric
esof
the
quar
ter
poun
dha
mbu
rger
sin
Japa
nw
ere
conv
erte
d
toU
.S.
doll
ars.
The
data
are
sum
mar
ized
inth
eta
ble
belo
w.
Sam
ple
mea
nS
ampl
est
anda
rdde
viat
ion
Sam
ple
size
U.S
.4.
530.
2415
Japa
n4.
010.
3810
Cal
cula
tea
99pe
rcen
tco
nfid
ence
inte
rval
for
the
diff
eren
cein
mea
npr
ice
for
aqu
arte
rpo
und
ham
burg
erin
the
Uni
ted
Sta
tes
and
Japa
n.
(A)
(4.5
3—
4.01
)±
3.o
12
J—.
+-
(B)
(4.5
3—
4.01
)+
3.0
12.J
-f±
—
(C)
(0.2
4—
0.38
)±
3.01
2((0
76)±
(O.3
8)(
62
))
(D)
(0.2
4—
0.38
)±
3.0
12J(0
24076)
+(O
.38)
(8.6
2)
(E)
(4.5
3—
4.01
)±
3.0
12J(0
24076)
+(O
.38
)(O
.62
)
4’ST
ATS
MED
IC
Unit 6 Practice Free Response Question
How much do Americans pay for coffee on average? In a 201 5 survey of 105 randomly selected U.S.adults, the respondents were asked what price they paid for their most recent purchase of coffee.The sample data had a mean of $3.42 and a standard deviation of $0.75.
(a) Construct and interpret a 95% confidence interval for the mean price paid for coffee in 201 5 by allU.S. adults.
.
(b) In 2013, tax receipts show that Americans paid an average of $2.98 per coffee. Do the 2015survey results provide convincing evidence that the average price Americans pay for coffee haschanged? Explain your reasoning.
+ STATS MEDIC
init 7 Free Response 2015 #4
4, A researcher conducted a medical study to investigate whether taking a low-dose aspirin reduces the chanceof developing colon cancer. As part of the study, l.(X)() adult volunteers were randomly assigned to one of twogroups. Half of the volunteers were assigned to the experimental group that took a 1owdose aspirin each day,and the other half were assigned to the control group that took a placebo each day. At the end of six years,15 of the people who took the low—dose aspirin had developed colon cancer and 26 of the people who tookthe placebo had developed colon cancer. At the significance level a = 0.05, do the data provide convincingstatistical evidence that taking a low-dose aspirin each day would reduce the chance of developing colon canceramong all people similar to the volunteers?
Sourco Copyright © The College Board.*AP is a registered trademark of the College Board, which was not involved in the production of, TATS IV! ED I Cand does not endorse, this product.
Unit 7 Free Response 2017 #5 .5. The table and the bar chart below summarize the age at diagnosis. in years. for a random sample of 207 men and
women currently being treated for schizophrenia.
0
I
AgeGroup (years)
Age-Group (years)
ID Men 0 WomenI
Do the data provide convincing statistical evidence of an association between age-group and gender in thediagnosis of schizophrenia?
.
Source: Copyright © The College Board.*AP is a registered trademark of the College Board, which was not iiwolved in the production of,
and does not endorse, this product. + STATS MEDIC
I I —I I
Women 46 40 2 I
20 to 2) 30 to 39 3() to 49 50 to 59 Total
1 1912
Men 53 23 9 3 8.
Total 99 63 30 15 207
20 to 29 30 to 39 40 to 49 50 to 59
Uni
t 7M
uftip
leC
hoic
e
1.A
Sta
tist
ics
clas
sfr
oma
high
scho
olw
ith4,
000
stud
ents
took
asu
rvey
ofth
efi
rst
35st
uden
tsw
ho
wal
ked
thro
ugh
the
fron
tdo
orof
the
scho
ol,
and
aske
dho
wfa
rth
eytr
avel
edto
scho
olth
atda
y.T
he
clas
spl
ans
toru
na
one-
sam
ple
t-te
stto
dete
rmin
eif
the
aver
age
trav
eldi
stan
ceha
sin
crea
sed
sinc
e
last
year
.T
hest
uden
tsno
tice
that
the
sam
ple
data
are
righ
tsk
ewed
.W
hich
cond
itio
nsha
vebe
en
sati
sfie
dfo
rth
et-
test
?
I.T
hesa
mpl
eis
from
ara
ndom
sam
ple
orra
ndom
ized
expe
rim
ent.
II.T
hesa
mpl
ing
dist
ribu
tion
ofsa
mpl
em
eans
isap
prox
imat
ely
norm
al.
Ill.
The
sam
ple
size
issm
all
rela
tive
toth
epo
pula
tion
.
(A)
Ill(B
)I a
ndII
(C)
I and
Ill
(D)
IIan
dIll
(E)
I,II,
and
Ill
2.A
nad
vert
iser
wan
tsto
find
conv
inci
ngev
iden
ceth
atte
levi
sion
view
ers
rem
embe
rm
ore
than
4
com
mer
cial
s,on
aver
age,
afte
rw
atch
ing
a30
min
ute
TVpr
ogra
m.
The
yta
kea
rand
omsa
mpl
eof
100
tele
visi
onvi
ewer
san
das
kth
emho
wm
any
com
mer
cial
sth
eyco
uld
rem
embe
raf
ter
wat
chin
ga
30m
inut
eTV
prog
ram
.T
heap
prop
riat
et-
test
was
cond
ucte
d,w
hich
resu
lted
ina
P-va
lue
of0.
15.
Ass
umin
gal
lco
ndit
ions
wer
em
et,
whi
chof
the
foll
owin
gis
anap
prop
riat
eco
nclu
sion
?
(A)
Bec
ause
the
P-va
lue
isle
ssth
an0.
05,
atth
e5%
sign
ific
ance
leve
l,th
ere
isno
tco
nvin
cing
evid
ence
that
tele
visi
onvi
ewer
sre
mem
ber
mor
eth
an4
com
mer
cial
s,on
aver
age,
afte
rw
atch
ing
a
30m
inut
eTV
prog
ram
.(B
)B
ecau
seth
eP-
valu
eis
gre
ater
than
0.05
,at
the
5%si
gnif
ican
cele
vel,
ther
eis
conv
inci
ng
evid
ence
that
tele
visi
onvi
ewer
sre
mem
ber
few
erth
an4
com
mer
cial
s,on
aver
age,
afte
rw
atch
ing
a
30m
inut
eTV
prog
ram
.
(C)
Bec
ause
the
P-va
lue
isgre
ater
than
0.01
,at
the
1%si
gnif
ican
cele
vel,
ther
eis
not
conv
inci
ng
evid
ence
that
tele
visi
onvi
ewer
sre
mem
ber
mor
eth
an4
com
mer
cial
s,on
aver
age,
afte
rw
atch
ing
a
30m
inut
eTV
prog
ram
.(D
)B
ecau
seth
eP-
valu
eis
gre
ater
than
0.01
,at
the
1%si
gnif
ican
cele
vel,
ther
eis
conv
inci
ng
evid
ence
that
tele
visi
onvi
ewer
sre
mem
ber
exac
tly
4co
mm
erci
als,
onav
erag
e,af
ter
wat
chin
ga
30
min
ute
TVpr
ogra
m.
(E)
Bec
ause
the
P-va
lue
isle
ssth
an0.
01,
atth
e1%
sign
ific
ance
leve
l,th
ere
isco
nvin
cing
evid
ence
that
tele
visi
onvi
ewer
sre
mem
ber
few
erth
an4
com
mer
cial
s,on
aver
age,
afte
rw
atch
ing
a30
min
ute
TVpr
ogra
m.
.,
..
3.A
fter
com
plet
ing
ast
atis
tica
lan
alys
isof
asu
rvey
of40
stud
ents
,th
epr
inci
pal
ofN
orth
Hig
h
Sch
ool
mad
eth
efo
llow
ing
conc
lusi
on:
reje
ctth
enu
llhy
poth
esis
;th
ere
isco
nvin
cing
evid
ence
that
mor
eth
an50
%of
stud
ents
supp
ort
asc
hedu
lech
ange
toha
velu
nch
occu
rea
rlie
rin
the
day.
Whi
ch
erro
rco
uld
have
been
com
mit
ted?
(A)
Typ
eIe
rror
:C
oncl
ude
that
mor
eth
an50
%of
stud
ents
wan
tea
rlie
rlu
nch,
whe
n50
%or
less
wan
t
earl
ier
lunc
h.(B
)T
ype
Ierr
or:
Con
clud
eth
atm
ore
than
50%
ofst
uden
tsw
ant
earl
ier
lunc
h,w
hen
mor
eth
an50
%
wan
tea
rlie
rlu
nch.
(C)
Typ
eII
erro
r:Fa
ilto
reje
ctth
at50
%of
stud
ents
wan
tea
rlie
rlu
nch,
whe
nm
ore
than
50%
wan
t
earl
ier
lunc
h.(D
)T
ype
IIer
ror:
Fail
tore
ject
that
50%
ofst
uden
tsw
ant
earl
ier
lunc
h,w
hen
50%
orle
ssw
ant
earl
ier
lunc
h.(E
)T
ype
IIer
ror:
Fail
tore
ject
that
mor
eth
an50
%of
stud
ents
wan
tea
rlie
rlu
nch,
whe
n50
%or
less
wan
tea
rlie
rlu
nch.
4.A
sign
ific
ance
test
was
cond
ucte
dus
ing
the
hypo
thes
esH
0:P
N—
PH
0,H
:P
N—
PH
<0
whe
re
PN
isth
etr
uem
ean
num
ber
offo
uls
call
eddu
ring
gam
espl
ayed
atne
utra
lsi
tes
and
PHis
the
true
mea
nnu
mbe
rof
foul
sca
lled
duri
ngga
mes
play
edat
the
hom
ete
am’s
stad
ium
with
are
sult
ing
P
valu
eof
0.24
.W
hich
ofth
efo
llow
ing
isan
accu
rate
inte
rpre
tati
onof
this
P-v
alue
?
(A)
The
reis
a24
%pr
obab
ilit
yth
atth
enu
llhy
poth
esis
istr
ue.
(B)
Ifth
ete
stw
ere
rep
eate
dm
any
tim
es,
we
wou
ldco
rrec
tly
reje
ctth
enu
llhy
poth
esis
24%
ofth
e
tim
e.(C
)If
the
test
wer
ere
pea
ted
man
yti
mes
,w
ew
ould
inco
rrec
tly
fail
tore
ject
the
null
hypo
thes
is24
%
ofth
eti
me.
(D)
Ifth
enu
llhy
poth
esis
istr
ue,
ther
eis
a24
%pr
obab
ilit
yof
gett
ing
asa
mpl
edi
ffer
ence
inm
eans
as
far
orfa
rthe
rbe
low
0as
the
diff
eren
cefo
und
inth
esa
mpl
es.
(E)
Ifth
enu
llhy
poth
esis
isfa
lse,
ther
eis
a24
%pr
obab
ilit
yof
gett
ing
asa
mpl
edi
ffer
ence
inm
eans
asfa
ror
fart
her
belo
w0
asth
edi
ffer
ence
foun
din
the
sam
ples
.
+ST
ATS
MED
IC4’
STAT
SM
EDIC
iiIii
11111it!”1111144444ggQg
9ggQ
.
‘p
a‘U
I:;;+ .
SIPtg1fl
‘p
+
10.
Bel
owis
com
pute
routp
ut
from
the
leas
tsq
uare
sre
gres
sion
anal
ysis
onth
ebo
dym
ass
inde
x,B
MI,
and
perc
ent
body
fat
for
10ra
ndom
lyse
lect
edad
ult
mal
es.
Whi
chof
the
foll
owin
gre
pres
ents
the
95%
conf
iden
cein
terv
alfo
rth
esl
ope
ofth
ere
gres
sion
line
rela
ting
BMI
and
perc
ent
body
fat
for
the
popu
lati
onof
adul
tm
ales
?
Pre
dict
orC
oef
SEC
oef
TP
Con
stan
t-2
0.09
62.
786
-7.2
130.
000
BMI
1.69
50.
2280
7.43
20.
000
S=
3.19
5R
-Sq
=87
.3%
R-S
q(ad
j)=
86.8
%
(A)
—20
.096
±2.
21(2
.786
)(B
)1.
695
±7.
432(
0.22
80)
(C)
1.69
5±
2.30
6(0.
2280
)(D
)1.
695
±2.
262(
0.22
80)
(E)
1.69
5±
2.22
8(0.
2280
)
11.
A20
-oun
ceso
dabo
ttle
issu
ppos
edto
cont
ain
20ou
nces
ofso
da.
The
dist
ribu
tion
ofth
eac
tual
amou
ntof
soda
ina
20-o
unce
soda
bott
leis
appr
oxim
atel
yno
rmal
.A
curi
ous
stu
den
tra
ndom
ly
sele
cts
fift
een
20-o
unce
soda
bott
les
from
vari
ous
reta
iler
san
dca
refu
llym
easu
res
thei
rco
nten
tto
see
ifth
eso
daco
mpa
nyis
chea
ting
the
cust
omer
s.T
hem
ean
and
stan
dard
devi
atio
nof
the
fift
een
bott
les
is19
.4ou
nces
and
0.25
ounc
es,
resp
ecti
vely
.W
hich
ofth
efo
llow
ing
isth
ete
stst
atis
tic
for
the
appr
opri
ate
test
tode
term
ine
ifth
eav
erag
eam
ount
ofso
dath
atis
cont
aine
din
thei
r20
-oun
ce
soda
bott
les
issi
gnif
ican
tly
less
than
20-o
unce
s?
12.
Ast
udy
cond
ucte
dby
apr
ofes
sor
atW
ayne
sbur
gU
nive
rsity
inve
stig
ated
whe
ther
tim
epe
rcep
tion
isim
pair
edw
hen
com
plet
ing
the
last
exam
ple
prob
lem
just
prio
rto
the
star
tof
fall
brea
k.
The
prof
esso
rti
med
how
long
itto
okto
com
plet
eth
ela
stex
ampl
epr
oble
m(in
seco
nds)
,th
enas
ked
ara
ndom
sam
ple
of10
stud
ents
toes
tim
ate
how
long
itto
okto
com
plet
eth
epr
oble
m(in
seco
nds)
.
Let
pre
pres
ent
the
aver
age
diff
eren
cein
time
(act
ual
time
—es
tim
ated
tim
e)it
took
toco
mpl
ete
the
prob
lem
for
all
stud
ents
.S
hew
ould
like
toin
vest
igat
ew
heth
erth
ere
will
beco
nvin
cing
stat
isti
cal
evid
ence
that
the
stud
ents
over
esti
mat
eth
eti
me
itto
okto
com
plet
eth
epr
oble
m,
onav
erag
e.
Whi
chof
the
foll
owin
gis
the
corr
ect
hypo
thes
esfo
rth
iste
st?
(A)H
o:p
=0andH
:p0
(B)H
o:p
=O
and
Ha:
p>
0
(C)H
o:u
=0andH
:p<
0
(D)H
o:p
>0andH
:p<
0
(E)H
o:p
<0andH
=0
13.
A21
-yea
rol
dco
lleg
est
uden
tsu
bmit
sa
phot
oto
the
web
site
“Gue
ssM
yA
ge”.
At
ala
ter
dat
ehe
chec
ksba
ckan
dth
ousa
nds
ofus
ers
have
mad
egu
esse
sab
out
his
age.
Of
the
foll
owin
g,w
hich
isth
ebes
tpr
oced
ure
toin
vest
igat
ew
heth
erth
ere
isco
nvin
cing
stat
isti
cal
evid
ence
that
,on
aver
age,
heis
perc
eive
dto
bele
ssth
an21
year
sol
d?
(A)
One
sam
ple
t-te
stfo
ra
mea
n(B
)O
nesa
mpl
ez-
test
for
apr
opor
tion
(C)
Mat
ched
-pai
rst-
test
for
am
ean
diff
eren
ce(D
)T
wo-
sam
ple
t-te
stfo
rth
edi
ffer
ence
betw
een
two
mea
ns
(E)
Ach
i-sq
uar
ete
sto
fas
soci
atio
n
14.
Stu
den
tsin
ast
atis
tics
clas
sw
ou
ldlik
eto
inves
tigat
eif
mor
eth
antw
o-t
hir
ds
ofth
eE
arth
isw
ater
.
To
answ
erth
isques
tion,
studen
tsto
ssed
anin
flat
able
glo
be
back
and
fort
h.A
fter
each
catc
h,
the
studen
tre
cord
edw
het
her
the
tip
ofth
eir
poin
ter
fin
ger
ofth
eir
righ
th
and
was
onw
ater
or
land
.In
50to
sses
,th
eir
fin
ger
was
onw
ater
38ti
mes
.A
ssum
ing
all
condit
ions
for
infe
ren
cear
em
et,
do
the
dat
ap
rov
ide
conv
inci
ngst
atis
tica
lev
iden
ceat
the
sign
ific
ance
leve
lof
a=
0.05
that
mor
eth
antw
o-
thir
dsof
the
Ear
this
wat
er?
(A)
Yes
,be
caus
eth
ep-
valu
eof
0.76
isgr
eate
rth
anth
esi
gnif
ican
cele
vel
of0.
05.
(B)
Yes
,be
caus
eth
ep-
valu
eof
0.08
isg
reat
erth
anth
esi
gnif
ican
cele
vel
of0.
05.
(C)
Yes
,be
caus
eth
ep-
valu
eof
0.05
isle
ssth
anth
esi
gnif
ican
cele
vel
of0.
08.
(D)
No,
beca
use
the
p-va
lue
of0.
08is
gre
ater
than
the
sign
ific
ance
leve
lof
0.05
.
(E)
No,
beca
use
the
p-va
lue
of0.
03is
less
than
the
sign
ific
ance
leve
lof
0.05
.
.
.,
.
19.4
—20
(A)
t=
,lT
t19
.4—
20(B
)z=
,j(O
.25)
(1_O
.25)
15
20—
19.4
(C)
t=
0.2
5)(
1-0
.25)
20
—1
9.4 19
.4—
20(E
)z=
(0.2
5)(0.7
5)(j+
)
+ST
ATS
MED
IC4’
STAT
SM
EDIC
15.
Acc
ordi
ngto
the
Nat
iona
lA
ssoc
iati
onof
Col
lege
san
dE
mpl
oyer
s,th
em
ean
sala
ryfo
ra
new
coll
ege
gra
du
ate
is$4
5,32
7.A
smal
lco
lleg
ew
ants
tokn
owif
the
mea
nsa
lary
ofth
eir
mos
tre
cent
grad
uate
sis
gre
ater
than
$45,
327.
Ara
ndom
sam
ple
of10
rece
ntgr
adua
tes
from
the
smal
lco
lleg
e
was
sele
cted
and
the
mea
nan
dst
anda
rdde
viat
ion
ofth
esa
lary
for
thos
egr
adua
tes
was
foun
d.W
ith
all
cond
itio
nsfo
rin
fere
nce
met
,a
sign
ific
ance
test
was
cond
ucte
dan
da
p-va
lue
of0.
045
was
obta
ined
.W
hich
ofth
efo
llow
ing
stat
emen
tsis
the
mos
tap
prop
riat
eco
nclu
sion
usin
ga
sign
ific
ance
leve
lof
a=
0.05
?
(A)
The
reis
conv
inci
ngst
atis
tica
lev
iden
ceth
atth
em
ean
sala
ryfo
ral
lre
cent
coll
ege
grad
uate
sfr
om
the
smal
lco
lleg
eis
gre
ater
than
$45,
327.
(B)
The
reis
conv
inci
ngst
atis
tica
lev
iden
ceth
atth
em
ean
sala
ryfo
rth
esa
mpl
eof
10co
lleg
e
grad
uate
sfr
omth
esm
all
coll
ege
isgr
eate
rth
an$4
5,32
7.
(C)
The
reis
not
conv
inci
ngst
atis
tica
lev
iden
ceth
atth
em
ean
sala
ryfo
ral
lre
cent
coll
ege
grad
uate
s
from
the
smal
lco
lleg
eis
gre
ater
than
$45,
327.
(D)
The
reis
not
conv
inci
ngst
atis
tica
lev
iden
ceth
atth
em
ean
sala
ryfo
rth
esa
mpl
eof
10co
lleg
e
grad
uate
sfr
omth
esm
all
coll
ege
isg
reat
erth
an$4
5,32
7.
(E)
The
reis
not
conv
inci
ngst
atis
tica
lev
iden
ceth
atth
egr
adua
tes
from
this
coll
ege
will
alw
ays
earn
mor
eth
an$4
5,32
7.
16.
Afi
nanc
ial
anal
yst
wan
tsto
inve
stig
ate
the
rela
tion
ship
betw
een
the
annu
alst
arti
ngsa
lary
ofne
w
empl
oyee
sat
ala
rge
firm
vers
usye
ars
ofed
ucat
ion
the
empl
oyee
has
(bey
ond
high
scho
ol).
The
anal
yst
sele
cted
ara
ndom
sam
ple
of18
new
empl
oyee
san
dre
cord
edth
eir
star
ting
sala
ryan
dho
w
man
yye
ars
ofed
ucat
ion
they
have
beyo
ndhi
ghsc
hool
.T
heco
mpu
ter
outp
utof
anan
alys
isof
sala
ry
vers
usye
ars
ofed
ucat
ion
issh
own
inth
eta
ble.
Reg
ress
ion
Ana
lysi
s:Sa
lary
(in$1
,000
)ve
rsus
Edu
cati
on
Pre
dic
tor
ConS
SE
Co
ef
TP
Consta
nt
25.8
40
3.8
03
Educati
on
13.4
862
0.5
310
Ass
umin
gth
atal
lco
ndit
ions
for
infe
renc
ear
em
et,
whi
chof
the
foll
owin
gis
the
app
rop
riat
ete
stst
atis
tic
for
test
ing
the
null
hypo
thes
isth
atth
esl
ope
ofth
epo
pula
tion
regr
essi
onlin
eeq
uals
0?
(A)
0
(B)
0.16
3
(C)
1
(D)
1.54
(E)
25.4
0
.
+ST
ATS
MED
IC
17.
At
the
coun
tyfa
irth
ere
are
man
yga
me
boot
hs.
One
boot
hha
sa
priz
e
whe
elw
ith8
equa
lse
ctor
s:2
ofw
hich
are
red,
2of
whi
char
ew
hite
,2
of
whi
char
eye
llow
,an
d2
ofw
hich
are
gree
n.It
cost
s$1
tosp
inth
ew
heel
.
The
rear
e4
poss
ible
“pri
zes”
.If
the
play
erla
nds
onon
eof
the
gree
n
sect
ors,
they
win
$5.
Ifth
eyla
ndon
aye
llow
sect
or,
they
win
asm
all
emoj
i
stuf
fed
toy.
Ifth
eyla
ndon
aw
hite
sect
or,
they
get
ati
cket
tori
deth
eFe
rris
whe
el.
Ifth
eyla
ndon
are
dse
ctor
,th
eyw
inno
thin
g.B
ecau
seyo
usu
spec
t
that
the
whe
elis
not
fair
,yo
uw
atch
ara
ndom
sam
ple
of10
0pe
ople
play
the
gam
e.H
ere
are
the
find
ings
: Col
orR
edW
hite
Gre
enY
ello
w
Obs
erve
d48
225
25
Exp
ecte
d25
2525
25
Ach
i-sq
uare
good
ness
offi
tte
stw
asco
nduc
ted
tode
term
ine
whe
ther
the
data
prov
ide
conv
inci
ng
evid
ence
that
the
whe
elis
not
fair
.T
hete
stst
atis
tic
was
37.5
2.W
hich
stat
emen
tis
twe?
(A)
At
the
sign
ific
ance
leve
la
=0.
05,
the
data
dono
tpr
ovid
eco
nvin
cing
evid
ence
that
the
whe
elis
not
fair
.
(B)
At
the
sign
ific
ance
leve
la
=0.
05,
the
data
prov
ide
conv
inci
ngev
iden
ceth
atth
ew
heel
isno
tfa
ir.
(C)
No
valid
conc
lusi
onca
nbe
mad
ebe
caus
eth
eob
serv
edfr
eque
ncy
for
one
cell
is5.
(D)
The
chi-
squa
rest
atis
tic
has
100—
1=
99d
egre
esof
free
dom
.
(E)
The
whe
elm
ayno
tbe
fair
,bu
tth
ega
me
isfa
irbe
caus
eal
lof
the
exp
ecte
dva
lues
are
equa
l.
18.
Acr
edit
card
com
pany
clai
ms
that
the
mea
nti
me
the
cust
omer
ssp
end
onho
ldis
3.5
min
utes
.
An
empl
oyee
ofth
isco
mpa
nybe
liev
esth
atcu
stom
ers
spen
dm
ore
than
3.5
min
utes
onho
ld.
A
rand
omsa
mpl
eof
rs=
36ca
llsis
sele
cted
and
the
mea
nti
me
the
cust
omer
sin
this
sam
ple
spen
ton
hold
was
5.15
min
utes
.A
llco
ndit
ions
for
infe
renc
ew
ere
met
and
the
p-va
lue
for
the
appr
opri
ate
hypo
thes
iste
stw
as0.
031.
Whi
chof
the
follo
win
gst
atem
ents
isth
ebe
stin
terp
reta
tion
ofth
ep
valu
e?
(A)
The
reis
a0.
031
prob
abil
ity
that
the
alte
rnat
ive
hypo
thes
isis
true
.
(B)
The
reis
a0.
031
prob
abil
ity
that
the
null
hypo
thes
isis
true
.
(C)
Ifth
enu
llhy
poth
esis
istr
ue,
ther
eis
a0.
031
prob
abil
ity
offi
ndin
gco
nvin
cing
evid
ence
that
5.15
min
utes
isg
reat
erth
an3.
5m
inut
es.
(D)
Ifth
enu
llhy
poth
esis
istr
ue,
the
prob
abil
ity
offi
ndin
gco
nvin
cing
evid
ence
that
the
null
hypo
thes
isis
true
is0.
031.
(E)
Ifth
enu
llhy
poth
esis
istr
ue,
the
prob
abil
ity
ofob
serv
ing
asa
mpl
em
ean
ofat
leas
t5.
15m
inut
es
is0.
031.
4’ST
ATS
MED
IC
.
.19
.A
mac
hine
that
mak
esdi
mes
isad
just
edto
mak
eth
emat
diam
eter
1.9
cm.
Pro
duct
ion
reco
rds
show
that
whe
nth
em
achi
neis
prop
erly
adju
sted
,it
will
mak
edi
mes
with
am
ean
diam
eter
of1.
9cm
and
with
ast
anda
rdde
viat
ion
of0.
1cm
.D
urin
gpr
oduc
tion
,an
insp
ecto
rch
ecks
the
diam
eter
sof
dim
esto
see
ifth
em
achi
neha
ssl
ippe
dou
tof
adju
stm
ent.
Ara
ndom
sam
ple
of64
dim
esis
sele
cted
.T
hein
spec
tor
wou
ldlik
eto
det
ect
ifth
etr
uem
ean
diam
eter
happ
ens
tore
ach
1.95
cmat
a
sign
ific
ance
leve
lof
a=
0.01
.H
ede
term
ines
the
pow
erof
this
test
tobe
0.92
28.
Wha
tis
the
prob
abil
ity
that
the
insp
ecto
rw
illm
ake
aT
ype
IIE
rror
?
(A)
0.01
(B)
0.03
85
(C)
0.05
(D)
0.07
72
(E)
0.92
28
20.
An
oran
geju
ice
man
ufac
ture
rad
vert
ises
ane
wor
ange
juic
epr
oduc
tth
atco
ntai
ns50
%le
ss
suga
r.T
his
new
prod
uct
isex
pec
ted
toin
crea
sepr
ofit
ssu
bsta
ntia
lly
beca
use
they
crea
teth
e50
%
less
suga
rpr
oduc
tby
repl
acin
g50
%of
the
juic
ew
ithw
ater
whi
lese
lling
itfo
rth
esa
me
pric
e.A
n
insp
ecto
rw
ants
toin
vest
igat
ew
heth
erth
eac
tual
per
centa
ge
ofw
ater
inth
epr
oduc
tis
with
in5%
of
the
inte
nded
50%
.H
ese
lect
sa
rand
omsa
mpl
eof
500
cont
aine
rsof
oran
geju
ice
and
dete
rmin
ed
the
per
cen
tag
eof
each
that
isw
ater
.H
epl
ans
toco
nduc
ta
sign
ific
ance
test
atth
ea
=0.
01le
vel
to
see
ifth
ere
isco
nvin
cing
evid
ence
that
the
prop
orti
onof
wat
erad
ded
isdi
ffer
ent
from
0.50
.W
hat
is
the
prob
abil
ity
that
the
insp
ecto
rm
akes
aT
ype
Ierr
or?
(A)
0.01
(B)
0.05
(C)0
.10
(D)
0.45
(E)
0.50
+ST
ATS
MED
IC
Unit 7 Practice Free Response Question
An online streaming service providing television programs claims that a 30-minute program willstream with advertisements that average 45 seconds. A consumer advocacy group is investigating tosee if this claim is true. They recorded the times of 21 randomly selected advertisements. The timesare listed below:
The mean and standard deviation for these times are 46.67 seconds and 2.78 seconds respectively.Do these data provide convincing evidence that the true mean advertisement length is longer than45 seconds?
.
.+ STATS MEDIC
Formulas for AP Statistics
Descriptive Statistics
— 1x = —x1 =n n
s =
___
- _)2 =
= a + bx
1
____ ____
n—I ç s ) s,
11. Probability and Distributions
= a + b
sb =
sx
III.
P(A u B) = P(A) + F(B) - P(A n B) P(A IB)= P(AnB)
Probability Distribution Mean Standard Deviation
Discrete random variable, X = E(X) = x1P(xii =(x. —p)2P(x.)
If X has a binomial distributionwith parameters n and p, then: = Jiip(1
—
p)
‘ ti — xP(X = x) = IflpX (1— p)
X)
where x = 0, 1, 2, 3, ,n
If X has a geometric distribution1 Ji—pwith parameter p, then: =; =x— 1 pP(X=x)=(1—p) p
where x = 1, 2, 3,
Sampling Distributions and Inferential Statistics
statistic — parameterStandardized test statistic:
standard error of the statistic
Confidence interval: statistic ± (critical value)(standard error of statistic)
Chi-square statistic: 2 = (observed — expected)2expected
III. Sampling Distributions and Inferential Statistics (continued)
Sampling distributions for proportions:
Random Parameters of Standard Error*
Variable Sampling Distribution of Sample Statistic
For onepopulation: p = p =
—
= l—n
Fortwo= Ifr1O_k1)+k2(1_2)
S. -populations: Ip1(1— p1) p2(l
—
p2) p1-p22 u. =1 +
l —
= p1 — p1_2 fl1 112
When p1 = p2 is assumed:
=O- )(!+±S.1P2 C fl flJ
— x1 +where fr —C
Sampling distributions for means:
Random Standard Error*Parameters of Sampling Distribution
f Sample StatisticVariable o
For one0 S
population: p = p cr-= - =
For twopopulations:
A1_X, — + = +
l— ‘2 - A2 S,?
- “2 fl1 fl2
Sampling distributions for simple linear regression:
Random Standard Error*Parameters of Sampling Distribution
Variable of Sample Statistic
SSb =
xFor slope: — U S ‘In —
- I-,
b x
2 where= (y
n-2where
X = 12 I(x. j2
and SX n—i
—
*Standard deviation is a measurement of variability from the theoretical population. Standard error is the estimate of the standard deviation. If thestandard deviation of the statistic is assumed to be known, then the standard deviation should be used instead of the standard error.
Table entry for is theprobability lying below
Table A Standard normal probabilities
z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
—3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002—3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003—3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005—3.1 .0010 .0009 .0009 .00009 .0008 .0008 .0008 .0008 .0007 .0007—3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010—2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014—2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019—2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026—2.6 .0047 .0045 .0044 .0043 .004! .0040 .0039 .0038 .0037 .0036—2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048—2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064—2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084—2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110—2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143—2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183— 1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .023 3—1.8 .0359 .035! .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294—1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367—1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455*1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559—1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681—1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823—1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985—1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170—1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379—0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611—0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867—0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148—0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451—0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776—0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3 156 .3121—0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483—0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859—0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247—0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641
Table entty for is theprobability lying below
.
Table A (Co,,tinued)
z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .53590.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .57530.2 .5793 .5832 .5871 5910 .5948 .5987 .6026 .6064 .6103 .6141
0.3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517(>.4 .6554 .6591 6628 .6664 .67000 .6736 .6772 .6808 .6844 .68790.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .72240.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .75490.7 .7580 .761 1 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .78520.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .81330.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .83891.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .86211.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .88301.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .90151.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .91771.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .93 191.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .94411,6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .95451.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .96331.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .97061.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .97672.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .98172.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .98572.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .98902.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .99 162.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .99362.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .99522.6 .9953 .9955 .9956 .9957 .9959 .9960 .996! .9962 .9963 .99642.7 .9965 .9966 .9967 .9968 .9969 .9970 .997! .9972 .9973 .99742.8 .9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .99812.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .99863.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .99903.! .9990 .9991 .999! .9991 .9992 .9992 .9992 .9992 .9993 .99933.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .99953.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .99973.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998
Table entry for p andC is the point t withprobability p lyingabove it andprobability C lyingbetween _t* and e.
Table B t distribution critical values
Tail probability p
df .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005
2345678
100t00000
1.000 1.376 t.963 3.078 6.314 12.71 15.89 31.82 63.66 127.3 318.3 636.6.816 l.06t 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.09 22.33 3t.60.765 .978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7.453 10.21 12.92.741 .941 1.190 t.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.610.727 .920 1.156 1.476 2.0t5 2.571 2.757 3.365 4.032 4.773 5.893 6.869.718 .906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959.711 .896 1,119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408.706 .889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041.703 .883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781.700 .879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587.697 .876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.025 4.437.695 .873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318.694 .870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221.692 .868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140.691 .866 1.074 1.341 1.753 2,131 2.249 2.602 2.947 3.286 3.733 4.073.690 .865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015.689 .863 1.069 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965.688 .862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.611 3.922.688 .861 1.066 1.328 1.729 2.093 2.205 2.539 2,861 3.174 3.579 3.883.687 .860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850.686 .859 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819.686 .858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792.685 .858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768.685 .857 1.059 1.318 1.711 2.064 2.172 2.492 2.797 3.091 3.467 3.745.684 .856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.078 3.450 3,725.684 .856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707.684 .855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 3.057 3.421 3.690.683 .855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408 3.674.683 .854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 3.038 3.396 3.659.683 .854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646.681 .851 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551.679 .849 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2,937 3.261 3.496.679 .848 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460.678 .846 1.043 1.292 1.664 1.990 2.088 2.374 2.639 2.887 3.195 3.416.677 .845 1.042 1.290 1.660 1.984 2.081 2.364 2.626 2.871 3.174 3.390.675 .842 1.037 1.282 1.646 1.962 2.056 2.330 2.581 2.813 3.098 3.300.674 .841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.091 3.291
50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9%
Confidence level C
Table entry for p is the point
(x2) with probability p lying
above it.
Table C ,2 critical values
109.1 111.7 114.7
.
(x2)
Tail probability p
df .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005
23456789
10111213141516171819202122232425262728293040506080
100
1,32 1.64 2.07 2.71 3.84 5.02 5.41 6.63 7.88 9.14 10.83 12.122.77 3.22 3.79 4.61 5.99 7.38 7.82 9.21 10.60 11.98 13.82 15.204.11 4.64 5.32 6.25 7.81 9.35 9.84 11.34 12.84 14.32 16.27 17.735.39 5.99 6.74 7.78 9.49 11.14 11.67 13.28 14.86 16.42 18.47 20.006.63 7.29 8.12 9.24 11.07 12.83 13.39 15.09 16.75 18.39 20.51 22.117.84 8.56 9.45 10.64 12.59 14.45 15.03 16.81 18.55 20.25 22.46 24.109.04 9.80 10.75 12.02 14.07 16.01 16.62 18.48 20.28 22.04 24.32 26.02
10.22 11.03 12.03 13.36 15.51 17.53 18.17 20.09 21.95 23.77 26.12 27.8711.39 12.24 13.29 14.68 16.92 19.02 19.68 21.67 23.59 25.46 27.88 29.6712.55 13.44 14.53 15.99 18.31 20.48 21.16 23.21 25.19 27.11 29.59 31.4213.70 14.63 15.77 17.28 19.68 21.92 22.62 24,72 26.76 28.73 31.26 33.1414.85 15.81 16.99 18.55 21.03 23.34 24.05 26.22 28.30 30.32 32.91 34.8215.98 16.98 18.20 19.81 22.36 24.74 25.47 27.69 29.82 31.88 34.53 36.4817.12 18.15 19.41 21.06 23.68 26.12 26.87 29.14 31.32 33.43 36.12 38.1118.25 19.31 20.60 22.31 25.00 27.49 28.26 30.58 32.80 34.95 37.70 39.7219.37 20.47 21.79 23.54 26.30 28.85 29.63 32.00 34.27 36.46 39.25 41.3120.49 21.61 22.98 24.77 27.59 30.19 31.00 33.41 35.72 37.95 40.79 42.8821.60 22.76 24.16 25.99 28.87 31.53 32.35 34.81 37.16 39.42 42.31 44.4322.72 23.90 25.33 27.20 30.14 32.85 33.69 36.19 38.58 40.88 43.82 45.9723.83 25.04 26.50 28.41 31.41 34.17 35.02 37.57 40.00 42.34 45.31 47.5024.93 26.17 27.66 29.62 32.67 35.48 36.34 38.93 41.40 43.78 46.80 49.0126.04 27.30 28.82 30.81 33.92 36.78 37.66 40.29 42.80 45.20 48.27 50.5127.14 28.43 29.98 32.01 35.17 38.08 38.97 41.64 44.18 46.62 49.73 52.0028.24 29.55 31.13 33.20 36.42 39.36 40.27 42.98 45.56 48.03 51.18 53.4829.34 30.68 32.28 34.38 37.65 40.65 41.57 44.31 46.93 49.44 52.62 54.9530.43 31.79 33.43 35.56 38.89 41.92 42.86 45.64 48.29 50.83 54.05 56.4131.53 32.91 34.57 36.74 40.11 43.19 44.14 46.96 49.64 52.22 55.48 57.8632.62 34.03 35.71 37.92 41.34 44.46 45.42 48.28 50.99 53.59 56.89 59.3033.71 35.14 36.85 39.09 42.56 45.72 46.69 49.59 52.34 54.97 58.30 60.7334.80 36.25 37.99 40.26 43.77 46.98 47.96 50.89 53.67 56.33 59.70 62.1645.62 47.27 49.24 51.81 55.76 59.34 60.44 63.69 66.77 69.70 73.40 76.0956.33 58.16 60.35 63.17 67.50 71.42 72.61 76.15 79.49 82.66 86.66 89.5666.98 68.97 71.34 74.40 79.08 83.30 84,58 88.38 91.95 95.34 99.61 102.788.13 90.41 93.11 96.58 101.9 106.6 108.1 1 12.3 116.3 120.1 124.8 128.3
1 18.5 124.3 129.6 131.1 135.8 140.2 144.3 149.4 153.2
Sta
tsM
edic
AP
Sta
tist
ics
Pra
ctic
eE
xam
ST
AT
IST
ICS
SE
CT
ION
1T
ime
—I
hour
and
30m
inut
esN
um
ber
ofqu
esti
ons
—40
Per
cent
ofto
tal
scor
e—S
0
Dir
ecti
ons:
Solv
eea
chof
the
foll
owin
gpr
oble
ms,
usin
gth
eav
aila
ble
spac
efo
rsc
ratc
hw
ork.
Dec
ide
whi
chis
the
best
choi
cegi
ven
and
fill
inth
eco
rres
pond
ing
circ
leon
the
answ
ersh
eet.
No
cred
itw
illbe
give
nfo
ran
ythi
ngw
ritt
enin
the
test
book
.D
ono
tsp
end
too
muc
hti
me
onan
yon
epr
oble
m
I.Sh
aron
isa
good
stud
ent
who
enjo
ysst
atis
tics.
She
sets
ago
alfo
rhe
rsel
fto
dow
ell
enou
ghco
mpa
red
tohe
rpe
ers
soth
athe
rst
anda
rdiz
edsc
ore
onhe
rS
tati
stic
sfi
nal
iseq
ual
tohe
rpe
rcen
tile
rank
(wri
tten
asa
deci
mal
)am
ong
her
clas
smat
es.
Wha
tgo
aldi
dsh
ese
tfo
rhe
rsel
f?
(A)0
.25
(B)
0.78
(C)
1.09
(D)2
.25
(E)2
.4l
2.In
ace
rtai
nre
gion
of
the
Uni
ted
Sta
tes,
the
dist
ribu
tion
of
the
num
ber
of
sibl
ings
anin
divi
dual
has
is
stro
ngly
skew
edto
the
righ
tw
itha
mea
nof
1.8
sibl
ings
.W
hich
of
the
foll
owin
gis
apo
ssib
leva
lue
for
the
med
ian
ofth
isdi
stri
buti
on?
(A)
1(B
)2(C
)3
(D)4
(E)
5
3.T
heph
rase
,ho
useh
old
pene
trat
ion,
desc
ribe
sth
epe
rcen
tage
of
hous
ehol
dsth
atpu
rcha
sea
part
icul
ar
item
.T
heho
useh
old
pene
trat
ion
for
toil
etpa
per
is97
%.
You
surv
eya
rand
omsa
mpl
eo
f50
hous
ehol
ds
and
wan
tto
com
pute
the
prob
abil
ity
that
atle
ast
one
ofth
eho
useh
olds
does
not
purc
hase
toil
etpa
per.
Whi
chof
the
foll
owin
gis
appr
opri
ate
for
mod
elin
gth
isdi
stri
buti
on?
(A)
Bin
omia
ldi
stri
buti
on(B
)G
eom
etri
cdi
stri
buti
on(C
)N
orm
aldi
stri
buti
on(D
)tdi
stri
buti
on(B
)C
hi-s
quar
edi
stri
buti
on
(A)
Incr
ease
the
conf
iden
cele
vel
to95
%.
(B)
Incr
ease
the
conf
iden
cele
vel
to99
%.
(C)
Incl
ude
aw
ider
dive
rsit
yo
fso
urce
s,su
chas
loca
lan
din
tern
atio
nal
new
sag
enci
es.
(0)
Incl
ude
new
sst
orie
sov
era
broa
dpe
riod
of
time,
such
asov
erth
epa
stde
cade
.
(B)
Incr
ease
the
sam
ple
size
.
5.A
ccor
ding
toa
repo
rt,
mor
ean
dm
ore
youn
gad
ults
are
drin
king
coff
eeda
ily.
An
inde
pend
ent
stud
y
cond
ucte
dus
ing
ara
ndom
sam
ple
of50
0yo
ung
adul
tspr
oduc
esa
95pe
rcen
tco
nfid
ence
inte
rval
forp
.
the
prop
orti
onof
all
youn
gad
ults
who
drin
kco
ffee
daily
.T
hein
terv
alw
asre
port
edto
be(0
.14,
0.18
).
Whi
cho
fth
efo
llow
ing
isco
rrec
t?
(A)T
hem
argi
no
fer
ror
for
the
give
nin
terv
alis
0.04
.
(B)
We
can
conc
lude
that
am
ajor
ity
of
youn
gad
ults
drin
kco
ffee
daily
.
(C)
The
reis
a95
%pr
obab
ilit
yth
atth
etr
uepr
opor
tion
ofy
oung
adul
tsth
atdr
ink
coff
eeis
betw
een
0.14
and
0.18
.(D
)We
can
be95
%co
nfid
ent
that
the
true
prop
orti
ono
fyo
ung
adul
tsth
atdr
ink
coff
eeda
ily
isbe
twee
n
0.l
4an
dO
.18.
(E)
Ifth
ispr
oced
ure
wer
eto
bere
peat
edm
any
tim
es,
95%
of
the
resu
ltin
gco
nfid
ence
inte
rval
sw
ill
disp
lay
that
the
true
prop
orti
onof
youn
gad
ults
that
drin
kco
ffee
daily
isbe
twee
n0.
14an
d0.
18.
6.T
hesu
pply
man
ager
ata
loca
lic
ecr
eam
shop
clai
ms
that
80%
of
cust
omer
spr
efer
choc
olat
eov
er
vani
lla.
One
ofth
eem
ploy
ees
beli
eves
that
isan
over
stat
emen
t.H
ese
lect
sa
rand
omsa
mpl
eo
f50
cust
omer
san
dfo
und
that
30o
fth
empr
efer
red
choc
olat
eov
erva
nilla
.W
hich
of
the
foll
owin
gis
the
appr
opri
ate
mar
gin
of
erro
rfo
ra
95pe
rcen
tco
nfid
ence
inte
rval
toes
tim
ate
the
popu
lati
onpr
opor
tion
of
all
cust
omer
sth
atpr
efer
choc
olat
eov
erva
nilla
?
(A)
I.645.0
60.
6)
(B)
I96
J(0.
SXi—
0.8)
(C)
I.96
(O.6
)O0.
6)
(D)
I9
6.0
808
)
(B)
2.5
76.J
(06
0.4)
:0
4.A
nor
gani
zati
onth
atst
rive
sto
hold
agen
cies
acco
unta
ble
for
trut
hin
new
sre
port
ing
plan
sto
sele
cta
rand
omsa
mpl
eo
f10
0ne
ws
stor
ies
from
maj
orU
Sne
ws
agen
cies
inor
der
toes
tim
ate
the
prop
orti
ono
f
new
sst
orie
spr
oduc
edby
maj
orU
.S.
new
sag
enci
esth
atco
ntai
nfa
lse
info
rmat
ion.
A90
perc
ent
conf
iden
cein
terv
alfo
rth
epr
opor
tion
of
all
new
sst
orie
sth
atco
ntai
nfa
lse
info
rmat
ion
will
then
be
cons
truc
ted.
Bef
ore
sele
ctin
gth
esa
mpl
e,th
eor
gani
zati
onde
term
ines
that
they
wan
tto
mak
eth
em
argi
n
of
erro
ras
smal
las
poss
ible
.W
hich
ofth
efo
llow
ing
isth
ebe
stw
ayfo
rth
emto
decr
ease
the
mar
gin
of
erro
r?
‘4’ST
ATS
MED
IC‘4’
STAT
SM
EDIC
7.P
rofe
ssor
Cha
uvet
has
6sn
ake
plan
tsat
her
hom
e.T
wo
are
smal
l,tw
oar
em
ediu
m,
and
two
are
larg
e.Sh
ew
ants
tose
eif
the
plan
tsw
illgr
owta
ller
ifth
eyar
egi
ven
wat
erfr
omhe
rfi
shta
nk.
She
puts
all
the
plan
tsin
her
bay
win
dow
atho
me
soth
eyre
ceiv
eeq
ual
amou
nts
ofsu
nlig
ht.
For
the
two
smal
lpl
ants
,sh
efl
ips
aco
into
dete
rmin
ew
hich
one
will
get
the
wat
erfr
omth
efi
shta
nk.
She
does
the
sam
efo
rth
e
med
ium
,an
dla
rge
plan
ts.
She
wat
ers
them
this
way
wee
kly
for
10w
eeks
.A
fter
10w
eeks
she
com
pare
sth
edi
ffer
ence
ingr
owth
for
each
set
of2
plan
ts.
Whi
cho
fth
efo
llow
ing
isth
ebe
stde
scri
ptio
no
fth
e
met
hod
she
isus
ing
for
data
coll
ecti
on7
(A)A
nob
serv
atio
nal
stud
y(B
)A
doub
le-b
lind
obse
rvat
iona
lst
udy
(C)
An
expe
rim
ent
with
aco
mpl
etel
yrs
ndom
ized
desi
gn(D
)An
expe
rim
ent
with
ara
ndom
ized
bloc
kde
sign
(E)
An
expe
rim
ent
with
am
atch
ed-p
airs
desi
gn
8.C
andi
date
Aan
dC
andi
date
Bar
eru
nnin
gfo
rpr
esid
ent
You
are
plan
ning
asu
rvey
tode
term
ine
wha
tpr
opor
tion
of
regi
ster
edvo
ters
plan
tovo
tefo
rC
andi
date
A(p
).Y
ouw
illco
ntac
ta
rand
omsa
mpl
eo
fre
gist
ered
vote
rs.
You
wan
tto
esti
mat
ep
with
99%
conf
iden
cean
da
mar
gin
of
erro
rno
grea
ter
than
0.01
.W
hat
isth
em
inim
umnu
mbe
ro
fre
gist
ered
vote
rsyo
uw
illne
edto
surv
eyin
orde
rto
mee
tth
ese
requ
irem
ents
9
(A)9
7(B
)16
6(C
)6,
766
(D)9
,604
(E)
16,5
90
9.A
gam
esh
owpr
oduc
eras
ked
100
rand
omly
sele
cted
adul
ts,
“Hav
eyo
uev
erbu
ngee
jum
ped?
”O
fth
ead
ults
surv
eyed
,14
said
“Yes
l”Is
ther
eco
nvin
cing
stat
isti
cal
evid
ence
that
the
true
prop
orti
ono
fal
lad
ults
that
have
bung
eeju
mpe
dis
mor
eth
an10
%?
(A)N
o.be
caus
eth
edi
ffer
ence
betw
een
the
sam
ple
prop
orti
onan
dth
epo
pula
tion
prop
orti
onis
only
0.04
,w
hich
isno
tgr
eate
rth
an0.
05.
(B)N
o,be
caus
eth
epr
obab
ility
’o
fob
serv
ing
asa
mpl
epr
opor
tion
atle
ast
asla
rge
as0.
14,
ifth
epo
pula
tion
prop
orti
onis
0.10
,is
grea
ter
than
0.05
.(C
)Y
es,
beca
use
the
prob
abil
ity
of
obse
rvin
ga
sam
ple
prop
orti
onat
leas
tas
larg
eas
0.14
,if
the
popu
lati
onpr
opor
tion
is0.
10,
isgr
eate
rth
an0.
05.
(D)
Yes
,be
caus
eth
epr
obab
ilit
yo
fob
serv
ing
asa
mpl
epr
opor
tion
atle
ast
asla
rge
as0.
14,
ifth
epo
pula
tion
prop
orti
onis
0.10
,is
less
than
0.05
(E)
Yes
,be
caus
eth
edi
ffer
ence
betw
een
the
sam
ple
prop
orti
onan
dth
epo
pula
tion
prop
orti
onis
0.04
,w
hich
isle
ssth
an00
5.
.
+ST
ATS
MED
IC
.
10.
Lin
dsey
isan
avid
tenn
ispl
ayer
.Sh
eke
pttr
ack
ofth
enu
mbe
rof
win
ners
she
had
per
gam
efo
ran
enti
re
seas
on.
The
shap
eo
fth
edi
stri
buti
onof
the
num
ber
ofw
inne
rsis
roug
hly
sym
met
ric
and
the
five
-
num
ber
sum
mar
yo
fth
enu
mbe
rof
win
ners
is:M
m:
10Q
i:18
Mcd
:48
Q3:
79M
ax:
92
Luk
eis
Lin
dsey
’sbi
gges
tri
val.
The
aver
age
num
ber
of
win
ners
Luk
eha
dpe
rga
me
for
the
seas
onha
sth
esa
me
valu
eas
Lin
dsey
’sIQ
R.
Who
had
the
grea
test
aver
age
num
ber
ofw
inne
rsth
isse
ason
?E
xpla
in.
(A)
Lin
dsey
,sh
eav
erag
edap
prox
imat
ely
48w
inne
rspe
rga
me
whi
leL
uke
only
aver
aged
18w
inne
rspe
rga
me.
(B)
Lin
dsey
,sh
eav
erag
edap
prox
imat
ely
49.4
win
ners
per
gam
ew
hile
Luk
eon
lyav
erag
ed48
win
ners
per
gam
e.(C
)L
uke.
heav
erag
ed61
win
ners
per
gam
ew
hile
Lin
dsey
only
aver
aged
appr
oxim
atel
y48
win
ners
per
gam
e.(D
)L
uke,
heav
erag
ed61
win
ners
per
gam
ew
hile
Lin
dsey
only
aver
aged
appr
oxim
atel
y79
win
ners
per
gam
e.(E
)T
here
isno
ten
ough
info
rmat
ion
prov
ided
tode
term
ine
Lin
dsey
’sav
erag
e.
II.
An
audi
tor
has
been
assi
gned
the
task
ofin
spec
ting
the
dice
used
ina
loca
lga
min
gre
sort
.A
fair
die
show
sa
6fa
ceup
one-
sixt
hof
the
time.
Inor
der
tode
term
ine
ifa
die
for
apa
rtic
ular
gam
eis
fair
,he
mus
tob
serv
ea
long
num
ber
of
tria
lsan
dre
cord
the
prop
orti
onof
the
time
that
the
die
land
ssh
owin
ga
6
faci
ngup
.T
hegr
aph
belo
wsh
ows
the
cum
ulat
ive
prop
orti
onof
sixe
sth
atar
ero
lled
for
100
cons
ecut
ive
tria
lsof
apa
rtic
ular
gam
e.045
Whi
cho
fth
efo
llow
ing
stat
emen
tsis
fals
e?
0.4
0.3
5
‘0.
3
0.2
5
0.2
-
a C0
1
1,1
00
5 0L
1—
________________
020
40
60
80
100
Num
berf
mats
(A)T
his
die
does
not
appe
arto
befa
irbe
caus
eit
appe
ars
that
the
prop
orti
ono
fsi
xes
from
this
part
icul
ardi
eis
abou
t0.
25.
(B)
Ifth
edi
eis
fair
,w
ew
ould
expe
ctto
see
the
long
-run
prop
orti
onof
sixe
sto
appr
oach
the
valu
e
0.16
7.(C
)T
hepr
obab
ilit
yof
roll
ing
asi
xca
nbe
esti
mat
edif
we
obse
rve
are
gula
ran
dpr
edic
tabl
epa
ttern
over
ave
rylo
ngse
ries
oftr
ials
(D)T
heau
dito
rob
serv
eden
ough
tria
lsto
draw
are
ason
able
conc
lusi
onab
out
the
fair
ness
oft
his
part
icul
ardi
e.(E
)T
his
die
appe
ars
tobe
fair
beca
use
the
prop
orti
onof
sixe
sfl
uctu
ates
grea
tly. +
STAT
SM
EDIC
b.
IP1It
1II‘1
IS
U‘I
Uii
III
It’llgggE
.E j‘a
+
‘6
0
2
+
18.
Ann
desi
res
togr
owta
llsu
nflo
wer
plan
tsSh
ew
onde
rsho
wth
eam
ount
ofw
ater
she
prov
ides
the
sunf
low
ers
will
affe
ctth
eir
grow
th.
One
spri
ngA
nnpl
ante
d25
sunf
low
erpl
ants
,m
akin
gsu
reea
chon
eha
dth
esa
me
soil,
amou
nto
fsp
ace,
and
expo
sure
tosu
nlig
ht.
The
firs
ton
ere
ceiv
edon
eou
nce
of
wat
erpe
rda
y.T
hese
cond
one
rece
ived
2ou
nces
of
wat
erpe
rda
y,an
dso
on.
To
dete
rmin
eth
eid
eal
amou
ntof
wat
erne
eded
,sh
eco
nsis
tent
lyw
ater
edhe
rsu
nflo
wer
sth
isw
ayan
dat
the
end
of
the
sum
mer
reco
rded
the
heig
hto
fea
chsu
nflo
wer
(in
cm).
The
nsh
epe
rfor
med
are
gres
sion
anal
ysis
onth
eda
ta.
Reg
ress
ion
Ana
lysi
s:H
eigh
tve
rsus
Am
ount
of
wat
erP
redi
ctor
Coe
fSE
Coe
fC
onst
ant
42.5
008.
340
5.10
Am
ou
nto
fwat
er5.
875
2.19
12.
68S
=8.
0527
R-S
q=
89.5
%R
-Sq(
adj)
=87
.2%
She
cond
ucts
asi
gnif
ican
cete
stto
dete
rmin
eif
ther
eis
conv
inci
ngev
iden
ceof
apo
siti
veli
near
rela
tion
ship
betw
een
the
amou
ntof
wat
erhe
rsu
nflo
wer
plan
tsre
ceiv
edan
dho
wta
llth
eygr
ew.
Wha
tis
the
corr
ect
test
stat
isti
can
dco
nclu
sion
?A
ssum
eal
lco
ndit
ions
for
infe
renc
ear
em
et.
(A)
t=2.
68.
The
reis
conv
inci
ngev
iden
ceof
apo
siti
veli
near
rela
tion
ship
betw
een
the
amou
ntof
wat
eran
dhe
ight
of
asu
nflo
wer
.(B
)t
=2.
68.
The
reis
not
conv
inci
ngev
iden
ceo
fa
posi
tive
line
arre
lati
onsh
ipbe
twee
nth
eam
ount
ofw
ater
and
heig
hto
fa
sunf
low
er.
(C)
1=
5.10
.T
here
isco
nvin
cing
evid
ence
of
apo
siti
velin
ear
rela
tion
ship
betw
een
the
amou
ntof
wat
eran
dhe
ight
ofa
sunf
low
er.
(D)1
=5.
10.
The
reis
not
conv
inci
ngev
iden
ceo
fa
posi
tive
line
arre
lati
onsh
ipbe
twee
nth
eam
ount
of
wat
eran
dhe
ight
of
asu
nflo
wer
.(E
)=
5.87
5.T
here
isco
nvin
cing
evid
ence
of a
posi
tive
line
arre
lati
onsh
ipbe
twee
nth
eam
ount
of
wat
eran
dhe
ight
ofa
sunf
low
er.
19.
Sam
isth
inki
ngab
out
swit
chin
gce
llph
one
prov
ider
s.Sa
mis
part
icul
arly
inte
rest
edin
mak
ing
sure
that
heha
sgo
odsi
gnal
stre
ngth
whe
nhe
isat
wor
k.H
eas
ksea
chof
his
30co
wor
kers
wha
tce
llph
one
prov
ider
they
use
and
ifth
eyha
vepo
orsi
gnal
stre
ngth
,m
oder
ate
sign
alst
reng
th,
orgo
odsi
gnal
stre
ngth
atw
ork.
Her
eis
ase
gmen
ted
bar
char
tof
the
resu
lts.
(A)A
llth
ree
prov
ider
sar
eeq
uall
ygo
odch
oice
sbe
caus
eal
lth
ree
bars
exte
ndto
I,or
100%
.
(B)O
ver
50%
of
his
cow
orke
rsdo
not
have
cell
serv
ice
whi
leat
wor
k.(C
)P
rovi
der
Bha
sm
uch
bett
ersi
gnal
stre
ngth
than
Pro
vide
rA
athi
sw
orkp
lace
.
(D)
Pro
vide
rA
has
repo
rts
ofth
egr
eate
stsi
gnal
stre
ngth
.(E
)P
rovi
der
Cha
sre
port
so
fth
egr
eate
stst
reng
thof
serv
ice.
20.
Whi
chof
the
foll
owin
gdi
stri
buti
ons
will
best
bem
odel
edby
ano
rmal
dist
ribu
tion
?
(A)A
bim
odal
dist
ribu
tion
with
spea
kat
3,a
peak
at10
,an
da
stan
dard
devi
atio
nof
5.
(B)A
unif
orm
dist
ribu
tion
with
am
ean
of5
for
whi
ch20
%o
fth
eob
serv
atio
nsar
ebe
twee
nI
and
3.
(C)
Abi
nom
ial
dist
ribu
tion
with
n=
150
and
p=
0.5.
(D)A
geom
etri
cdi
stri
buti
onw
ithp
=0.
9.(E
)A
chi-
squa
redi
stri
buti
onw
ith2
degr
ees
offr
eedo
m.
.
4’ST
ATS
MED
IC
e
+ST
ATS
MED
IC
...
TP
0.00
00.
005
80.0
%
700
%
Goo
d.*
rnü
Mod
.oto
noI
Oro
ogib
t’oor
ogoo
140on
th
60.0
%
5011
%
40.0
%
300%
•
200%
0.0%
Pro
voiA
i’ro
ooir
rji
Proo
,doo
CG
roop
Whi
chof
the
foll
owin
gst
atem
ents
issu
ppor
ted
byth
eda
ta?
21.
Aco
lleg
epr
ofes
sor
reco
rded
the
spee
dw
ithw
hich
stud
ents
ran
out
the
door
afte
rcl
ass
afte
rta
king
the
fina
lex
am(u
sing
ara
dar
gun)
for
each
ofth
ela
st4
sem
este
rs.
The
hist
ogra
mbe
low
show
sth
edi
stri
buti
onof
spee
dfo
r16
8st
uden
ts.
The
max
imum
valu
eis
18m
ph.
30 01
23
45
57
89
10
11
12
13
18S
eec1
fmp
h)
The
valu
e,18
mph
,w
asac
tual
lysu
ppos
edto
be8m
phan
dth
iser
ror
isco
rrec
ted
Whi
cho
fth
efo
llow
ing
istr
ue? (A
)The
mea
nw
illch
ange
the
sam
eam
ount
asth
anth
em
edia
n,an
dth
era
nge
will
chan
geth
esa
me
amou
ntas
the
SD.
(B)T
hem
ean
will
chan
gem
ore
than
the
med
ian,
and
the
rang
ew
illch
ange
mor
eth
anth
eSD
.(C
)T
hem
edia
nw
illch
ange
mor
eth
anth
em
ean,
and
the
rang
ew
illch
ange
mor
eth
anth
eSD
.
(D)T
hem
ean
will
chan
gem
ore
than
the
med
ian,
and
the
SDw
illch
ange
mor
eth
anth
era
nge.
(E)
The
med
ian
will
chan
gem
ore
than
the
mea
n,an
dth
eSD
will
chan
gem
ore
than
the
rang
e.
22.
Sup
pose
that
the
McA
flis
te?s
purc
hase
d15
plan
eti
cket
sfo
ran
upco
min
gfa
mily
trip
toPa
ris.
Eac
hti
cket
inde
pend
entl
yha
sa
0.01
prob
abil
ity
of
bein
gac
cide
ntal
lyth
row
naw
ay.
Wha
tis
the
prob
abil
ity
that
exac
tly
one
of
the
tick
ets
isac
cide
ntal
lyth
row
naw
ay?
(A)(-)
(0.0
1)
(B)
(0.0
1)i
(0•9
9)i
4
(C)
(0.0
lXl)
+(0
.99X
l4)
(D)
15(0
.01
)‘(0
.99)
’(E
)15
(0.0
1)‘
(0.9
9)’
..
...
24.
The
rear
efo
rty
mul
tipl
e-ch
oice
ques
tion
son
this
exam
,ea
chha
ving
answ
erch
oice
sA
,B
,C
,D
.or
E.O
nly
one
answ
erch
oice
per
ques
tion
isco
rrec
t.S
uppo
sea
stud
ent
rand
omly
gues
ses
thei
ran
swer
choi
ceto
each
ques
tion
,an
dth
eir
gues
ses
from
ques
tion
toqu
esti
onar
ein
depe
nden
t.W
hich
ofth
efo
llow
ing
is
the
prob
abil
ity
that
the
stud
ent
gues
ses
atle
ast
12qu
esti
ons
corr
ectl
yon
this
port
ion
of
the
exam
?
(A)0
.023
8(B
)0.
0442
(C)
0.08
75(D
)0.9
125
(E)
0.98
06
25.
Res
earc
hers
are
usin
ga
new
fitn
ess
wat
chw
ithhe
art
mon
itor
ing
capa
bili
ties
tost
udy
the
hum
anhe
art.
Inpa
rtic
ular
,th
eyar
eex
amin
ing
the
rela
tion
ship
betw
een
the
pres
ence
of
arrh
ythm
ias,
orir
regu
lar
hear
tbea
ts,
and
stre
ss.
Ara
ndom
sam
ple
of10
0w
omen
betw
een
the
ages
of
30an
d50
wer
ese
lect
edfo
r
ast
udy.
At
the
begi
nnin
go
fth
est
udy,
each
wom
anco
mpl
eted
aqu
esti
onna
ire
that
clas
sifi
edth
emas
havi
nghi
ghor
low
stre
ss.
Eac
hw
oman
was
also
give
na
fitn
ess
wat
chto
wea
rfo
rI
wee
k.T
hew
atch
esre
veal
edto
the
rese
arch
ers
whe
ther
each
wom
anha
da
hear
tar
rhyt
hmia
.T
hefo
llow
ing
tabl
egi
ves
the
num
ber
ofw
omen
that
fall
into
each
cate
gory
.
Low
stre
ssH
igh
stre
ssII
5225
12
Bas
edon
thes
eda
ta,
whi
cho
fth
efo
llow
ing
conc
lusi
ons
ism
ost
appr
opri
ate?
(A)T
here
isev
iden
ceth
athi
ghst
ress
caus
eshe
art
arrh
ythm
ias,
and
the
conc
lusi
onca
nbe
gene
rali
zed
toal
lw
omen
aged
30to
50.
(B)
The
reis
evid
ence
that
high
stre
ssca
uses
hear
tar
rhyt
hmia
s,an
dth
eco
nclu
sion
can
bege
nera
lize
dto
all
wom
enag
ed30
to50
who
wea
ra
titn
ess
wat
ch.
(C)
The
reis
evid
ence
that
high
stre
ssca
uses
hear
tar
rhyt
hmia
s.an
dth
eco
nclu
sion
can
bege
nera
lize
dto
all
wom
ensi
mil
arto
thos
ein
the
stud
y.(D
)Alt
houg
hca
use-
and-
effe
ctca
nnot
bees
tabl
ishe
d,th
ere
isan
asso
ciat
ion
betw
een
stre
ssan
dth
e
pres
ence
ofhe
art
arrh
ythm
ias
for
the
popu
lati
ono
fal
lw
omen
aged
30to
50.
(E)
Alt
houg
hca
use-
and-
effe
ctca
nnot
bees
tabl
ishe
d,th
ere
isan
asso
ciat
ion
betw
een
stre
ssan
dth
epr
esen
ceof
hear
tar
rhyt
hmia
sfo
rth
epo
pula
tion
ofal
lw
omen
.
23.
Ara
ndom
vari
able
Xha
sth
efo
llow
ing
dist
ribu
tion
:x
—2
02
4P(
X)
2c4c
0.3
0.1
Wha
tis
the
expe
cted
valu
eof X
?
(A)0
.l(B
)0.2
(C)0
.4(D
)0.6
(E)0
.8
25 20 15 10
Arr
hyth
mia
sN
oar
rhyt
hmia
s
+ST
ATS
MED
IC.
STAT
SM
EDIC
26.
Hav
eyo
uev
erru
nin
toso
meo
neyo
ukn
oww
hen
you
wer
efa
raw
ayfr
omho
me?
Ara
ndom
sam
ple
of
1000
adul
tsw
ere
aske
dth
isqu
esti
on.
Her
ear
eth
eir
resp
onse
s
Res
pons
eN
umbe
ro
fre
spon
ses
Yes
—m
ore
than
once
87
Yes
—on
etim
e11
2
No
801
Bas
edon
the
resp
onse
s,w
hich
ofth
efo
llow
ing
isa
90pe
rcen
tco
nfid
ence
inte
rval
for
the
prop
orti
ono
f
all
adul
tsw
how
ould
resp
ond
that
they
have
run
into
som
eone
they
know
whe
nth
eyw
ere
far
away
from
hom
e9
(A) 0
.087
±0.
0147
(6)0
.087
±0.
0175
(C)
0.19
9±
0.02
08(D
)0.1
99
±0
.02
47
(E)0
.801
±0.
0325
27.
Aco
inis
wei
ghte
dso
that
the
prob
abil
ity
of
head
s(H
)is
grea
ter
than
the
prob
abil
ity
ofta
ils(T
).W
hich
oft
hefo
llow
ing
orde
rsis
the
mos
tpr
obab
le?
(A)H
HH
(B)
TT
T(C
)TH
T(D
)HT
H(E
)T
TH
28.
The
Uni
ted
Stat
esPo
stal
Ser
vice
deli
vers
man
ypa
ckag
esev
ery
day.
Apo
stal
carr
ier
reco
rded
the
num
ber
of
pack
ages
hede
live
red
each
day
for
92da
ys.
Eac
hda
yha
da
uniq
uenu
mbe
rof
pack
ages
deli
vere
d(n
odo
uble
s)H
ere
are
the
resu
lts.
Mea
n11
0S
tand
ard
Dev
iatio
n:24
.25
Qi:
75M
edia
n:98
Q3:
122
How
man
yda
ysdi
dhe
deli
ver
few
erth
an75
pack
ages
?
(A)7
(B)2
3(C
)25
(D)3
5(E
)46
29.
An
epid
emio
logi
stw
asca
lled
upon
toin
vest
igat
ea
case
offo
odpo
ison
ing
ata
com
pany
picn
ic.
Aft
erin
terv
iew
ing
ISO
of
the
atte
ndee
s,th
eep
idem
iolo
gist
cons
truc
ted
the
foll
owin
gta
ble.
Food
Poi
soni
ng?
Ate
the
Pota
toSa
lad?
Yes
No
Yes
7218
90
No
852
60
Tot
al80
7015
0
Let
Abe
the
even
tth
ata
rand
omly
sele
cted
pers
onat
eth
epo
tato
sala
d.L
etB
beth
eev
ent
that
a
rand
omly
sele
cted
pers
ongo
tfo
odpo
ison
ing.
Whi
chof
the
foll
owin
gst
atem
ents
isco
rrec
t?
(A)P
(AI
B)=
P(A
)(B
)E
vent
sA
and
Bar
ede
pend
ent.
(C)
Eve
ntA
caus
esev
ent
B.
(D)E
vent
Aan
dE
vent
Bar
em
utua
lly
excl
usiv
e.(E
)P(A
and
B)>
P(A
orB
)
30.
Afi
shst
ore
empl
oyee
reco
rded
the
num
ber
of
babi
esbo
rnto
each
of20
diti
eren
tfi
sh.
The
data
and
sum
mar
yst
atis
tics
are
show
nbe
low
.
089
12455578899
20
11
46
322
41
Key
:0j
8re
pres
ents
afi
shth
atga
vebi
rth
to8
babi
es.
Var
iabl
eC
ount
Mea
nSE
Mea
nSt
Dev
Mm
QI
Med
ian
Q3
Bab
ies
2020
.31
864
8.33
68
1518
.525
Ifth
eem
ploy
eew
ere
tora
ndom
lyse
lect
one
of
thes
efi
sh,
wha
tis
the
prob
abil
ity
that
itw
ould
have
had
few
erth
an5
babi
es?
(A)0
.2(B
)0.
25(C
)0.2
62(D
)0.3
5(E
)0.7
5
.
+ST
ATS
MED
IC
.
+ST
ATS
MED
IC
.,
Tot
al Max
41
I31
Acu
riou
sac
coun
tant
ata
larg
efi
rmw
ould
like
tokn
owif
mon
eyca
nbu
yha
ppin
ess.
She
sele
cts
ara
ndom
sam
ple
of
30of
her
wea
lthy
clie
nts
and
cont
acte
dth
emto
ask
“On
asc
ale
of
1-10
0,ho
wha
ppy
are
you?
”T
here
sult
ing
95pe
rcen
tco
nfid
ence
inte
rval
for
the
true
mea
nha
ppin
ess
rati
ngfo
ral
lw
ealt
hycu
stom
ers
is(6
75
,89
.5).
Whi
chof
the
foll
owin
gst
atem
ents
best
sum
mar
izes
the
mea
ning
of
95%
conf
iden
ce?
(A) A
ppro
xim
atel
y95
%of
the
wea
lthy
cust
omer
sin
the
surv
eyre
port
edha
ving
happ
ines
sra
ting
sbe
twee
n67
.5an
d89
.5.
(B)A
ppro
xim
atel
y95
%of
the
wea
lthy
cust
omer
sat
this
firm
have
happ
ines
sra
ting
sbe
twee
n67
.5an
d89
.5.
(C)
Aw
ealt
hycu
stom
erse
lect
edat
rand
omfr
omth
ispo
pula
tion
has
aha
ppin
ess
rati
ngbe
twee
n67
.5an
d89
.595
%of
the
time.
(D)A
bout
95%
of
all
rand
omsa
mpl
esof
30w
ealt
hycu
stom
ers
from
this
popu
lati
onw
ould
resu
ltin
a95
perc
ent
conf
iden
cein
terv
alof
(67.
5,89
.5)
(E)
Abo
ut95
%of
all
rand
omsa
mpl
esof
30w
ealt
hycu
stom
ers
from
this
popu
lati
onw
ould
resu
ltin
a95
perc
ent
conf
iden
cein
terv
alth
atca
ptur
esth
epo
pula
tion
mea
nha
ppin
ess
ratin
g.
32.
The
auth
orof
anar
ticl
eab
out
proc
rast
inat
ion
inth
ew
orkp
lace
clai
med
that
,on
aver
age,
empl
oyee
sw
aste
2ho
urs
per
day
surf
ing
the
Inte
rnet
,te
xtin
g,an
dc-
mai
ling
frie
nds
duri
ngw
ork
hour
s.S
uppo
seth
eC
EO
of
ala
rge
com
pany
wan
tsto
dete
rmin
ew
heth
erth
em
ean
was
ted
time
duri
ngan
8-ho
urw
ork
day
for
empl
oyee
sof
her
com
pany
isle
ssth
anth
em
ean
of
120
min
utes
repo
rted
inth
ear
ticle
.Sh
ese
lect
sa
rand
omsa
mpl
eof
10em
ploy
ees
from
the
com
pany
.E
ach
of
the
10em
ploy
ees
was
call
edin
toth
eC
EO
’sof
fice
and
she
aske
dth
emto
esti
mat
eho
wm
uch
time
(in
min
utes
)th
eyty
pica
lly
was
ted
per
day
whi
leat
wor
ksu
rfin
gth
ein
tern
et,
text
ing,
and
emai
ling
frie
nds.
The
esti
mat
eo
fth
eam
ount
oftim
ew
aste
dby
empl
oyee
sat
this
com
pany
is
(A)
likel
yto
bean
unde
rest
imat
eof
the
beca
use
of
unde
rcov
erag
e.(B
)lik
ely
tobe
anun
dere
stim
ate
ofth
etr
uth
beca
use
of
resp
onse
bias
.(C
)lik
ely
tobe
anov
eres
tim
ate
of
the
beca
use
of
unde
rcov
erag
e.(D
)lik
ely
tobe
anov
eres
tim
ate
of
the
trut
hbe
caus
eof
resp
onse
bias
.(E
)lik
ely
tobe
fair
lyac
cura
tebe
caus
eth
eem
ploy
ees
wer
era
ndom
lyse
lect
ed.
33.
Wha
tis
the
prop
erw
ayto
inst
all
aro
llof
toil
etpa
per:
the
“ove
r”po
siti
on,
inw
hich
the
port
ion
you
grab
hang
sov
erth
eto
pof
the
roll,
orth
e“u
nder
”po
siti
on,
inw
hich
the
port
ion
you
grab
hang
sun
der/
behi
ndth
ero
ll?A
curi
ous
stud
ent
inve
stig
ated
this
ques
tion
byas
king
ara
ndom
sam
ple
of
10cu
stod
ians
and
ara
ndom
sam
ple
of
50ad
ults
that
are
not
cust
odia
ns.
The
tabl
esu
mm
ariz
esth
ere
sults
:
they
are
acu
stod
ian,
give
n
.-34
.A
stat
isti
cste
ache
rcr
eate
da
hom
ewor
kco
mpl
etio
nin
cent
ive
prog
ram
.If
ast
uden
tco
mpl
etes
all
of
thei
r
hom
ewor
kfo
rth
een
tire
chap
ter,
thei
rna
me
isw
ritt
enon
the
boar
din
anu
mbe
red
list.
The
nth
ete
ache
rse
lect
s5
nam
esfr
omth
elis
t,w
itho
utre
plac
emen
t,us
ing
ara
ndom
num
ber
gene
rato
ran
daw
ards
thos
e
stud
ents
with
aho
mew
ork
pass
.W
hat
type
ofsa
mpl
edi
dth
ete
ache
rse
lect
?
(A)a
conv
enie
nce
sam
ple
(B)a
stra
tifi
edra
ndom
sam
ple
from
the
popu
lati
onof
all
stud
ents
that
did
and
did
not
com
plet
eth
eho
mew
ork
(C)
asy
stem
atic
rand
omsa
mpl
e(D
)asi
mpl
era
ndom
sam
ple
from
the
popu
lati
onof
all
stud
ents
that
com
plet
edth
eho
mew
ork
(E)
asi
mpl
era
ndom
sam
ple
from
the
popu
lati
onof
all
stud
ents
inth
ecl
ass
35.
All
day
labo
rers
of
ala
rge
man
ufac
turi
ngco
mpa
nyre
ceiv
ea
2%ra
ise
ever
y6
mon
ths.
The
curr
ent
mea
nho
urly
wag
eea
rned
byth
eal
lda
yla
bore
rsis
$9.7
5pe
rho
uran
dth
est
anda
rdde
viat
ion
of
thei
rho
urly
wag
esis
$0.8
7pe
rho
ur.
Ass
umin
gth
atth
era
ise
rate
and
freq
uenc
yre
mai
nth
esa
me,
wha
tw
illth
em
ean
and
stan
dard
devi
atio
no
fth
eho
urly
wag
esea
rned
byda
yla
bore
rsbe
2ye
ars
from
now
?
(A)
Mea
n=
$0.7
8,S
tand
ard
devi
atio
n$0
.07
(B)
Mea
n=
$10.
55,
Stan
dard
devi
atio
n=
$0.8
7(C
)M
ean
=$1
0.55
,S
tand
ard
devi
atio
n=
$0
94
(D)M
ean
=$2
0.22
,S
tand
ard
devi
atio
n$0
.87
(E)
Mea
n=
$20.
22,
Sta
ndar
dde
viat
ion
=$1
.80
36.
Acc
ordi
ngto
loya
ltyca
rdda
ta,
the
amou
nto
fm
oney
spen
tpe
rsh
oppe
rat
the
groc
ery
Stor
eIS
norm
ally
dist
ribu
ted
with
am
ean
of
S75
per
trip
and
ast
anda
rdde
viat
ion
of
$25
per
trip
.H
owm
uch
mon
eydo
es
ash
oppe
rsp
end
that
isat
the
95ui
perc
enti
leo
fth
isdi
stri
buti
on?
(A) $
25.0
0(B
)$33
88(C
)$5
0.00
(D)$
l16
.12
(E)
$125
.00
Cus
todi
anI
Non
-Cus
todi
anA
dult
(A)8
/40
(B)
8/50
(C)
8/60
(D)1
6/40
(E)
16/I
00
+ST
ATS
MED
IC+
STAT
SM
EDIC
37.
Am
anuf
actu
rer
ofal
l-in
-one
prin
ters
isco
ncer
ned
that
the
war
rant
yco
sts
for
apa
rtic
ular
prin
ter
mod
elex
ceed
the
amou
ntex
pect
edby
the
com
pany
.B
ased
ona
revi
ewo
fco
mpl
eted
war
rant
ycl
aim
s,th
edi
stri
buti
ono
fth
ew
arra
nty
cost
per
clai
mis
skew
edto
the
righ
tw
ithm
ean
$150
and
stan
dard
devi
atio
n
S50.
Ara
ndom
sam
ple
of25
com
plet
edw
arra
nty
clai
ms
isse
lect
ed,
and
the
sam
ple
mea
nco
stis
reco
rded
.S
uppo
seth
epr
oces
sof
sele
ctin
ga
rand
omsa
mpl
eof
25co
mpl
eted
arr
an
tycl
aim
san
dre
cord
ing
the
sam
ple
mea
nco
stis
repe
ated
for
ato
tal
of
100
sam
ples
Whi
cho
fth
efo
llow
ing
best
desc
ribe
sa
dotp
lot
crea
ted
from
the
100
sam
ple
mea
ns?
(A)T
hedo
tplo
tha
sth
esa
me
shap
eas
the
dist
ribu
tion
of
the
popu
lati
onw
ithm
ean
$150
and
stan
dard
devi
atio
n$2
5.(B
)T
hedo
tplo
tha
sth
esa
me
shap
eas
the
dist
ribu
tion
of
the
popu
lati
onw
ithm
ean
$150
and
stan
dard
devi
atio
n$5
0.(C
)T
hedo
tplo
tha
sth
esa
me
shap
eas
the
dist
ribu
tion
of
the
popu
lati
onw
ithm
ean
$150
and
stan
dard
devi
atio
n$1
00.
(D)T
hedo
tplo
tis
clos
erto
appr
oxim
atel
yno
rmal
than
the
dist
ribu
tion
ofth
epo
pula
tion
with
mea
n$1
50an
dst
anda
rdde
viat
ion
$10.
(E)
The
dotp
lot
iscl
oser
toap
prox
imat
ely
norm
alth
anth
edi
stri
buti
ono
fth
epo
pula
tion
with
mea
n$1
50an
dst
anda
rdde
viat
ion
$50.
38.
The
Am
eric
anH
eart
Ass
ocia
tion
rand
omly
sele
cted
100
adul
tm
ales
and
emai
led
them
asu
rvey
that
aske
dtw
oqu
esti
ons:
“Hav
eyo
uev
erex
peri
ence
da
hear
tat
tack
?”an
d“A
reyo
ure
ligi
ous?
”.O
fth
ose
that
wer
ese
ntth
esu
rvey
38co
mpl
eted
the
surv
ey.
Wha
tar
eth
epo
pula
tion
and
the
sam
ple
ofth
isst
udy9
(A)T
hepo
pula
tion
isth
eIO
Uad
ult
mal
es,
and
the
sam
ple
isth
e38
adul
tm
ales
that
com
plet
edth
esu
rvey
.
40.
Asc
hool
dist
rict
dete
rmin
esth
em
ean
and
the
stan
dard
devi
atio
nof
the
num
ber
of
days
that
stud
ents
of
the
dist
rict
are
abse
ntfo
rth
ela
stqu
arte
rof
the
scho
olye
ar.
Whi
chof
the
foll
owin
gis
the
best
desc
ript
ion
ofth
est
anda
rdde
viat
ion?
(A)
The
stan
dard
devi
atio
ngi
ves
the
appr
oxim
ate
med
ian
dist
ance
betw
een
the
mea
nnu
mbe
rof
days
abse
ntfo
rth
ese
stud
ents
and
the
num
ber
ofda
ysab
sent
byth
ein
divi
dual
stud
ents
.
(B)
The
stan
dard
devi
atio
ngi
ves
the
tota
ldi
stan
cebe
twee
nth
em
ean
num
ber
ofda
ysab
sent
tbr
thes
est
uden
tsan
dth
enu
mbe
ro
fda
ysab
sent
byth
ein
divi
dual
stud
ents
.
(C)
The
stan
dard
devi
atio
nde
scri
bes
the
vari
abil
ity
ofth
em
iddl
e50
%o
fth
edi
stri
buti
on,
orth
edi
stan
cebe
twee
nth
efi
rst
and
thir
dqu
arti
lefo
rth
enu
mbe
ro
fda
ysab
sent
byth
ein
divi
dual
stud
ents
.
(D)T
hest
anda
rdde
viat
ion
desc
ribe
sth
eva
riab
ilit
yof
the
mid
dle
95%
of
the
dist
ribu
tion
,or
the
dist
ance
betw
een
all
num
ber
of
days
abse
ntth
atar
ew
ithin
2st
anda
rdde
viat
ions
ofth
em
ean.
(E)
The
stan
dard
devi
atio
ngi
ves
the
appr
oxim
ate
mea
ndi
stan
cebe
twee
nth
em
ean
num
ber
of
days
abse
ntfo
rth
ese
stud
ents
and
the
num
ber
of
days
abse
ntby
the
indi
vidu
alst
uden
ts.
(B)T
hepo
pula
tion
isth
e10
0ad
ult
mal
es,
and
the
sam
ple
isal
lad
ult
mal
esfo
rw
hom
the
resu
lts
can
bege
nera
lize
d.(C
)T
hepo
pula
tion
isal
lad
ult
mal
es,
and
the
sam
ple
isth
e38
adul
tm
ales
that
com
plet
edth
esu
rvey
.(D
)The
popu
lati
onis
all
adul
tm
ales
,an
dth
esa
mpl
eis
the
100
adul
tm
ales
that
wer
ese
lect
edto
rece
ive
the
surv
ey.
(E)
The
popu
lati
onis
all
adul
tm
ales
,an
dth
esa
mpl
eis
ifth
eyex
peri
ence
da
hear
tat
tack
orno
tan
dw
heth
eror
not
they
are
relig
ious
.
39.
Inth
epo
pula
rm
ovie
,“B
ack
toth
eFu
ture
”D
r.E
mm
ett
Bro
wn
told
Mar
tyM
cFly
,“D
on’t
wor
ry.
As
long
asyo
uhi
tth
atw
ire
with
the
conn
ecti
ngho
okat
prec
isel
y88
mile
spe
rho
urth
ein
stan
tth
eli
ghtn
ing
stri
kes
the
tow
er.
.ev
eryt
hing
will
befi
ne.”
Ass
ume
the
prob
abil
ity
that
Mar
tyhi
tsth
ew
ire
with
the
conn
ecti
ngho
okis
0.8.
Giv
enth
athe
hits
the
wir
ew
ithth
eco
nnec
ting
hook
,th
epr
obab
ilit
yth
athe
does
soat
prec
isel
y88
mil
espe
rho
uris
0.10
.G
iven
that
hehi
tsth
ew
ire
atpr
ecis
ely
88m
iles
per
hour
,th
epr
obab
ilit
yth
atth
isal
lha
ppen
sth
ein
stan
tth
eli
ghtn
ing
stri
kes
the
tow
eris
0.02
.W
hat
isth
epr
obab
ilit
yth
at“e
very
thin
gw
illbe
fine
”?
(A)0
.001
6(B
)0.
0800
(C)
0.40
00(D
)0.8
020
(E)
0.92
00
.
4.ST
ATS
MED
IC
a
‘4.S
TATS
MED
IC
..,
STATISTICSSECTION!!
Part AQuestions 1-5
Spend about 65 minutes on this part of the exam.Percent of Section II score — 75
Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on thecorrectness of your methods as well as on the accuracy and completeness of your results and explanations.
1. A tech company claims that its new smart watch takes heart monitoring to the next level. A study wasconducted to measure and compare the resting heart rates with active heart rates for adults aged 30-50. Arandom sample of 20 adults aged 30-50 were selected for study.
The participants met at a local hospital for study. They were all given a smart watch and asked to sit andread for 15 minutes. During that time their resting heart rate was measured. Then they went to a fitnesscenter. They were asked to jog around the track as many times as they could in 5 minutes. During this timetheir active heart rates were measured. The back-to-back stemplot below displays the resting and activeheart rates for the participants.
Resting Active988553 6
8744100 77550 8
10 95 10
1112 025513 6814 258815 1225816 2899171819 5
Key: 12j0 represents a participant with an active heart rate of 120 beats per minute
(a) Write a few sentences comparing the distribution of the resting and active heart rates for theseparticipants.
+ STATS MEDIC
(b) The researchers would like to calculate the amount of increase from resting to active heart rate for each
person in order to identify potential health problems that typically go undetected. Is the information
provided in the back-to-back stemplot sufficient for investigating this relationship? Explain
(c) Researchers created the following table which identifies the age of the participant along with their
resting and active heart rates. A scatterplot displaying the relationship between age and difference in
heart rate is also shown.
ge (years) 30 30 32 34 35 38 40 41 41 45 45 45 46 46 47 48 48 48 49 49
Resting 63 70 70 65 80 71 65 85 74 68 68 85 69 74 90 77 78 87 91 95
(bpm)kctive(bpm) 120 136 122 125 138 195 151 142 145 125 152 162 148 148 152 155 168 158 169 169
Difference 57 66 52 60 58 124 86 57 71 57 84 77 79 74 62 78 90 71 78 74
C
a)
Based on the scatterplot, describe the relationship between age and the difference in resting and active heartrate?
+ STATS MEDIC
.130
120e
110
100
90 a80
70
60
50’
40 1
30 35 40
Age (years)
I
•. I.. .
aa ‘
45 50
The manufacturers of a new running shoe, Blast Off, claim that a new insole material acts as a springboard,launching the runner forward with every step. Researchers would like to determine if there is a difference inthe mean speed for runners wearing Blast Off compared to a traditional shoe. They plan to conduct a studywith 100 runners.
A random sample of 50 male runners who report that they wear the shoe, Blast Off, and random sample of50 male runners that run with other shoes will be selected. The researchers ask each of the 100 runners fortheir fastest 1-mile time on a track and recorded the responses. They will then compare the mean runningspeed for the two groups.
(a) Is this an observational study or an experiment? Explain.
(b) Explain the concept of confounding in the context of this study. Include an example of a possibleconfounding variable.
(c) If the mean running speed for those who wear Blast Off is statistically significantly faster than the meanrunning speed for runners wearing other shoes, could one conclude that the faster running speed iscaused by wearing Blast Off shoes? Explain.
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3. Due to concerns about the underinflation of footballs, the National Football League (NFL) created a seriesof standards that must be met for the weight, length, and the long and short circumferences of each ball. It ( Dstated that the balls are to be inflated to between 12.5 to 13.5 pounds. The pressure output by the ball pumpis approximately Normal with a mean of 13 pounds and a standard deviation of 0.25 pounds. At each game,the home team must supply 12 balls to the referee 2 hours and 15 minutes prior to the start of the game forinspection.
(a) What is the probability that a randomly selected ball will not meet the inflation specifications?
(b) Assuming that the mean amount of inflation is 13 pounds and that all 12 balls are independently tested.What is the probability that at least one of the 12 balls will not meet the inflation specifications?
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(c) If the home team wants to be 99 percent certain that a randomly selected ball will be withinspecifications, what is the largest standard deviation in pressure that is acceptable for the ball pump?
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Amy and Brayden each drive from their apartment building to the gym to exercise before going to work.They leave at the same time, so traffic conditions are the same. They disagree about which of 2 routes isthe quickest to get from their building to the gym. Amy thinks route A is faster and Brayden thinks route Bis faster. They took a random sample of 10 days and recorded the travel times for both routes. Their traveltimes are provided in the table.
1 2 3 4 5 6 7 8 9 10Route A
21.3 18.8 19.5 19.4 21.4 20.7 22.6 20.7 21.2 19.5(mm)Route B
20.5 18.3 19.7 19.3 20.6 20.2 23.6 18.1 19.1 18.2(mm)Difference
0.8 0.5 —0.2 0.1 0.8 0.5 —1.0 2.6 2.1 1.3(A — B)
Do the data provide convincing evidence that, on average, route B is faster than route A?
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5. An article claims that the distribution of eye color is 79% brown, 8% blue, 5% hazel, 5% amber, 2% green,and 1% other. A random sample of 500 adults were selected and 55 had blue eyes.
(a) Construct and interpret a 90 percent confidence interval for the proportion of adults that have blue eyes.
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(b) Use your confidence interval in part (a) to comment on the belief that 8 percent of people have blueeyes.
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Question 6Spend about 25 minutes on this part of the exam.
Percent of Section II score — 25
Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on thecorrectness of your methods as well as on the accuracy and completeness of your results and explanations.
6. The amount of time that Alyse procrastinates after school follows a normal distribution. Alyseprocrastinates less than 10 minutes 10% of the time and she procrastinates more than 60 minutes 60% of thetime.
(a) The provided normal distribution has marks at the mean, as well as 1, 2, and 3 standard deviations awayfrom the mean. Estimate and label the location of the boundary and shade the area corresponding to eachof the statements:
i. “Alyse procrastinates less than 10 minutes 10% of the time.”
ii. “She procrastinates more than 60 minutes 60% of the time.”
(b) Determine the value of the z-score corresponding to each of the following statements, then interpret thez-score:
i. “Alyse procrastinates less than 10 minutes 10% of the time.”
ii. “She procrastinates more than 60 minutes 60% of the time.”
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STATISTICSSECTION II
Part B
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I
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(c) The mean u and the standard deviation a of the distribution of the amount of time that Alyse7
procrastinates after school are unknown. Use your responses in part (b) to write an equation for each ofDthe z-scores for the following statements:
i. “Alyse procrastinates less than 10 minutes 10% of the time.”
ii. “She procrastinates more than 60 minutes 60% of the time.”
(d) Use your equations from part (c) to determine the mean number of minutes and the standard deviation ofthe number of minutes that Alyse procrastinates after school?
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