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How many U.S. Presidents can YOU name in a minute?. AP Stat Project #1 May 16, 2011 – Block 1 John Graziano & Lydia Keener. Introduction. Record: Gender Last Social Studies class Grade in last Social Studies class One minute to name as many U. S. presidents, verified by complete list - PowerPoint PPT Presentation
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AP STAT PROJECT #1MAY 16 , 2011 – BLOCK 1
JOHN GRAZIANO & LYDIA KEENER
How many U.S. Presidents can YOU name in a minute?
Introduction
Record: Gender Last Social Studies class Grade in last Social Studies class
One minute to name as many U. S. presidents, verified by complete list
Purpose: To see whether or not Social Studies class taken, gender, and grade in SS class correlate with number of presidents named
We want to see how many presidents YOU truly know!
Who is this man? (HINT: He’s a
president!)
Graph
1
2
3
4
5
6
7
Pres0 5 10 15 20 25 30
Collection 1 Histogram
Shape: Right SkewedCenter: Median (11)Spread: Range – 18
IQR – 3.5
Collection 1
Pres
12.31254.11478
79.5111325
S1 = meanS2 = sS3 = minS4 = Q1S5 = medianS6 = Q3S7 = max
Normal Model?
-2
-1
0
1
2
Pres0 5 10 15 20 25 30
Normal Quantile = 0.243Pres - 3
Collection 1 Normal Quantile Plot
Normal Probability Plot is linear, therefore the data is normal.
Quantitative Data by GenderF
M
Pres6 8 10 12 14 16 18 20 22 24 26
Collection 1 Box PlotCollection 1
RowSummary
Gender
M
Gender
F
Pres
4.399467
10.511.5
132520
12.75
3.6545979
10.513.5
1812
11.5833
4.114787
9.511132532
12.3125S1 = sS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = countS8 = mean
MaleShape: Slightly Right SkewedCenter: Median (10.5)Spread: Range – 18
IQR – 2.5
FemaleShape: Approx. Normal w/ 3 OutliersCenter: Median (11.5)Spread: Range – 11
IQR – 4.5
Quantitative Data by PartnerLy
dia
McN
elis
Pres0 5 10 15 20 25 30
Collection 1 Box Plot Collection 1
RowSummary
Partner
McNelis
Partner
Lydia
Pres
12.7083247
10121425
4.40828
11.125899
10.511.5
182.99702
12.3125327
9.5111325
4.11478S1 = meanS2 = countS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s
LydiaShape: Approx. Normal w/ 2 OutliersCenter: Median (12)Spread: Range – 18
IQR – 4
McNelisShape: Abnormal and Right SkewedCenter: Median (10.5)Spread: Range – 9
IQR – 2.5
Quantitative Data by Partner cont.
PLEASE NOTE:McNelis’s boxplot looks abnormal due to the
fact that she collected far less data than Lydia.
Quantitative by Social Studies GradeA
BC
Pres5 10 15 20 25
Collection 1 Box Plot
Collection 1
RowSummary
SS_GradeSS_Grade
B C
SS_Grade
A
Pres
11.8159
10111319
2.70449
12.81251679
11.516.5
255.25635
121
1212121212
#Evaluation error#
12.312532
79.5111325
4.11478S1 = meanS2 = countS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s
Quantitative by Social Studies Grade cont.
Grade AShape: Slightly Right Skewed w/ 1 OutlierCenter: Median (11)Spread: Range – 10
IQR – 3
Grade BShape: Very Right SkewedCenter: Median (11.5)Spread: Range – 18
IQR – 7.5
Grade CNo shape, center, or spreadOne ValueAbnormal Data
Who is this m
an?
(HINT: He’s also a
president)
Two-Way Table
Collection 1
RowSummary
Column Summary
SS_GradeSS_Grade
B C
SS_Grade
A
F
MGender
12 8 0
3 8 1
15 16 1
20
12
32S1 = count
Marginal Distribution for Gender
Males: 62.2%Females: 37.5%
2468
10121416182022
GenderF M
count
Collection 1 Bar Chart
Marginal Distribution for SS Grade
A: 46.875%B: 50%
C: 3.125%
2
4
6
8
10
12
14
16
18
SS_GradeA B C
count
Collection 1 Bar Chart
Conditional Distribution
Collection 1
RowSummary
Column Summary
SS_GradeSS_Grade
B C
SS_Grade
A
F
M
Gender
120.6
80.4
00
30.25
80.666667
10.0833333
150.46875
160.5
10.03125
201
121
321
S1 = countS2 = row proportion
Of the Females:-60% got A’s-40% got B’s-0% got C’s
Of the Males:-25% got A’s-67% got B’s-8% got C’s
Gender vs. # of Presidents
Gen
der
0
2
4
6
8
10
12
14
F
2
4
6
8
10
12
14
M
SS_GradeA B C
count
Collection 1 Bar Chart
Chi-Squared Test for Independence - Gender
First attribute: Gender Number of categories: 2Second attribute: Pres Number of categories: 13
Warning: 26 out of 26 cells have expected values less than 5.
Alternative hypothesis: There is an association betw een Gender and Pres
The test statistic, chi-square, is 13.23. There are 12 degrees of freedom (the number of row s minus one times the number of columns minus one).
If it w ere true that Gender w ere independent of Pres (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be 0.35.
The numbers in parentheses in the table are expected counts.
RowSummary
Column Summary
M
Gender
F
7
8
9
10
11
12
13
15
16
18
19
21
25
Pres
1 (1.2) 1 (0.8)
0 (0.6) 1 (0.4)
3 (3.1) 2 (1.9)
1 (1.9) 2 (1.1)
5 (3.8) 1 (2.2)
3 (3.1) 2 (1.9)
3 (1.9) 0 (1.1)
0 (0.6) 1 (0.4)
1 (0.6) 0 (0.4)
0 (1.2) 2 (0.8)
1 (0.6) 0 (0.4)
1 (0.6) 0 (0.4)
1 (0.6) 0 (0.4)
20 12
2
1
5
3
6
5
3
1
1
2
1
1
1
32
Even though our sample suggested Gender and
Number of Presidents to be dependent, our Chi-Squared
Test for independence of population determined that
the difference was not substantial enough to deem it
dependent.
SS Grade vs. # of PresidentsSS
_Gra
de
0123456
A
0123456
B
123456
C
Pres0 5 10 15 20 25 30
Collection 1 Histogram
Chi-Squared Test for Independence – SS Grade
Test of Collection 1 Test for Independence
First attribute (categorical): Pres
Second attribute (categorical): SS_Grade
First attribute: Pres Number of categories: 13Second attribute: SS_Grade Number of categories: 3
Warning: 39 out of 39 cells have expected values less than 5.
Alternative hypothesis: There is an association betw een Pres and SS_Grade
The test statistic, chi-square, is 19.52. There are 24 degrees of freedom (the number of row s minus one times the number of columns minus one).
If it w ere true that Pres w ere independent of SS_Grade (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be 0.72.
The numbers in parentheses in the table are expected counts.
RowSummary
Column Summary
PresPresPresPresPresPresPresPresPresPresPresPres
8 9 10 11 12 13 15 16 18 19 21 25
Pres
7
A
B
C
SS_Grade
0 (0.9) 0 (0.5) 3 (2.3) 1 (1.4) 5 (2.8) 2 (2.3) 2 (1.4) 0 (0.5) 1 (0.5) 0 (0.9) 1 (0.5) 0 (0.5) 0 (0.5)
2 (1.0) 1 (0.5) 2 (2.5) 2 (1.5) 1 (3.0) 2 (2.5) 1 (1.5) 1 (0.5) 0 (0.5) 2 (1.0) 0 (0.5) 1 (0.5) 1 (0.5)
0 (0.1) 0 (0.0) 0 (0.2) 0 (0.1) 0 (0.2) 1 (0.2) 0 (0.1) 0 (0.0) 0 (0.0) 0 (0.1) 0 (0.0) 0 (0.0) 0 (0.0)
2 1 5 3 6 5 3 1 1 2 1 1 1
15
16
1
32
Chi-Squared Test for Independence – SS Grade Cont.
Both the bar graph and the Chi-Squared test for
independence for SS grade/
# of Presidents show that the two variable are independent of each
other.
Error and Bias
Sources of error: Commotion of room not
allowing people ultimate concentration ability
Individuals over-hearing presidents from previous rounds
Both partners had a list of presidents during every trial except their own
Time to think about presidents before their turn
Who is this m
an?
(HIN
T: He’s p
robably
going to be
president)
Conclusion
From our data, we can conclude that the data is normal. We can also conclude that because of the small sample size, the variable of gender and # of
presidents are independent, even though they appear dependent in our data. The variables of SS
grade and # of presidents, however, were determined to be independent of each other. The median of # of presidents named in our data was 11 presidents and 50% of subjects know at least
10-13 presidents.Who is this beautiful lady? (HINT: She’s probably not
going to be president)