AP Statistics

Has been about the distribution of sample means

and the distribution of the difference of sample means.

and the distribution of sample proportions

1 2

2 21 2

1 2

ˆ

xz

n

xts n

x xt

s s

n n

p pz

pqn

1 2

1 2

1 2

2 21 2

1 2

ˆ

ˆ

x

x

x x

x x

p

p

n

n n

p

pq

n

1 2 1 2

1 2 1 2

1 2

ˆ ˆ ˆ ˆ 1 2

1 1 2 22 2 2ˆ ˆ ˆ ˆ

1 2

1 1 2 2ˆ ˆ

1 2

1 1 2 2

1 1

1 1

Formula for std dev true only if independence

condition is met: pop >10 & pop >10

p p p p

p p p p

p p

p p

p p p p

n n

p p p p

n n

n n

If these conditions are met, the sampling distribution of difference of proportions is approximately normal

1 1

1 1

2 2

2 2

ˆ 5

ˆ 5

ˆ 5

ˆ 5

n p

n q

n p

n q

1 1 2 2

1 2

*1 2

ˆ ˆ ˆ ˆ1 1

ˆ ˆ

p p p pSE

n n

CI p p z SE

Researchers want to test the effectiveness of a new anti-anxiety medication. In clinical testing, 64 out of 200 people taking the medication report symptoms of anxiety. Of the people receiving a placebo, 92 out of 200 report symptoms of anxiety. Construct a 95% confidence interval for the true difference in the proportion of people reporting anxiety on the placebo and drug.

1: Populations & Parameter of Interest

2: Procedure Name & Conditions

3: Calculations

4: Interpret

Two-Proportion Z intervalResearchers want to test the effectiveness of a new anti-anxiety medication. In clinical testing, 64 out of 200 people taking the medication report symptoms of anxiety. Of the people receiving a placebo, 92 out of 200 report symptoms of anxiety. Construct a 95% confidence interval for the true difference in the proportion of people reporting anxiety on the placebo and drug.

1: Population, Parameter of Interest,H0 and Ha

2: Procedure Name & Conditions

3: Calculations

4: Interpret

0 1 2

1 2

1 2

1 2

:

:a

H p p

H

p p

p p

p p

1 2

1 2

1 1 2 2

1 2

ˆ ˆ

1 1ˆ ˆ1

where

ˆ ˆˆ

p pz

p pn n

n p n pp

n n

Two-Proportion Z Test

Researchers want to test the effectiveness of a new anti-anxiety medication. In clinical testing, 64 out of 200 people taking the medication report symptoms of anxiety. Of the people receiving a placebo, 92 out of 200 report symptoms of anxiety. Is the medication working any differently than the placebo? Test this claim at the 5% significance level.v

Two-Proportion Z Test

1: Population, Parameter of Interest,H0 and Ha

2: Procedure Name & Conditions

3: Calculations

4: Interpret

Two-Proportion Z Test

Researchers want to test the effectiveness of a new anti-anxiety medication. In clinical testing, 64 out of 200 people taking the medication report symptoms of anxiety. Of the people receiving a placebo, 92 out of 200 report symptoms of anxiety. Is the medication working any differently than the placebo? Test this claim at the 5% significance level.