Formula Sheet Non-cumulative Final F2011

8/3/2019 Formula Sheet Non-cumulative Final F2011

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Final Exam, BU/EC255, Fall 2011

Formulae and Statistical Tables Booklet

Non-Cumulative Version

INSTRUCTIONS

1. Nothing may be written on or in this formula booklet, other than your name and

number.

2. Any student found with anything written on or in the formula booklet during a test or

exam will have the entire booklet confiscated.

3. Additionally, students may be subject to proceedings under the university's

regulations on academic honesty.

4. Students must use their own booklet

Name:


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Inference about One Population

CI of when is known

nzx 2 /

CI of when is unknown

1, / 2n

s x t

n

CI of p

/ 2 (1 ) / p z p p n

Sample size to estimate when is known

2

/ 2 zn E

= ; If is unknown, approximate using Range/4.

Sample size to estimate p

2 / 2

2

(1 ) p p zn

E =

Test statistic for testing when is known

/

x z

n

=

Test statistic for testing when is unknown

Test statistic for testing p

1n

xt

s n

=


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Inference about Two Populations

z-test of 1111 2222 when population variances are known:

( ) ( )1 2 1 22 2

1 2

1 2

x x z

n n

=

+

CI of 1 2: known variances

( )2 2

1 21 2

1 2 / 2 z x x n n

+

t-test of 1111 2222 when population variances are unknown but equal:

1 2 2n nt + =

( ) ( )1 2 1 2

1 2

1 1 p

x x

sn n

+,

( ) ( )

2nn

s1ns1ns

21

222

2112

p

+

+=

CI of 1 2: unknown but equal variances

1 21 2 2, / 2

1 2

1 1( ) *n n p x x t s n n +

+

t-Test of D

1 /

n

d

d Dt

s n

=

CI of D

1, / 2d

n

sd t

n

T f


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CI of p 1 p 2

( )2

22

1

112 / 21 n

)p1(pn

)p1(pzpp +

One-Way ANOVA Table

2

1

( )C

i ii

SSC n x x=

=

2

1( 1)

C

i ii

SSE n s=

=

Simple (k=1) and Multiple (k 2) Regression Analysis

Standard Error of Estimate

2eSSE

Sn

=

Coefficient of determination

2

YY

SSR RSS

=

Adjusted 2 R :

2 2 /( 1) 11 1 (1 )/( 1) 1 A

SSE n k n R R

SS n n k

= =


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ANOVA Table

Testing the Slope Coefficient i

1

i

i in k

b

bt

s

=

CI ofi

/2, 1* ii n k bb t s

For Simple Regression Analysis ONLY

Confidence Interval for average Y:

( )20 / 2, 2

1 * *SSn e xx

X X Y t S

n

+

Prediction Interval for individual Y:

( )20 / 2, 2

1 * * 1SSn e xx

X X Y t S

n

+ +

Test Statistic for Chi-squared tests:


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Table A.5 Areas of the Standard Normal Distribution


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Table A.6 critical Values from the t Distribution


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10

Table Chi-squared Distribution

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Formula Sheet Non-cumulative Final F2011