Section 12.2 Comparing Two Proportions

Shaquille O'Neal has made 53.3% of his free throws over his career, during this past offseason he worked with a free throw coach and then started out the next season making 26 of 39 free throws.

a) Is this evidence that Shaq has significantly improved his free throw shooting ability?

b) Describe a Type I and Type II error in this situation.

Section 12.2Comparing Two Proportions

March 30th 2009

Difference between two distribution

2 2 2

X Y X Y

X Y X Y

0 1 2 1 2

1 2 1 2

: 0

: 0a

H p p p p

H p p p p

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

p p p p

p p p p

p p

p p p p

n n

Difference between two distribution

2 2 2

X Y X Y

X Y X Y

0 1 2 1 2

1 2 1 2

: 0

: 0a

H p p p p

H p p p p

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

ˆ ˆ

ˆ ˆ ˆ ˆ1 1

p p p p

p p p p

p p

p p p p

n n

Two proportion confidence interval

1 1 2 2

1 2

*1 2

1 1 1 1 2 2 2 2

ˆ ˆ ˆ ˆ1 1

ˆ ˆ

Populations are at least 10

times the samples and

ˆ ˆ ˆ ˆ5, 1 5, 5, 1 5

p p p pSE

n n

CI p p z SE

n p n p n p n p

Accept or reject?

We understand with normal variation and everything working normally, we will get a sodium value between 1.9723 mg and 2.0277 mg 95% of the time.

0.12 1.96

502 .0277,2 .0277

1.9723,2.0277

Accept or reject?

We understand with normal variation and everything working normally, we will get a sodium value between 1.9723 mg and 2.0277 mg 95% of the time.

This means the 5% of the time you will reject a batch of chips that are fine.

When we reject the batch (and H0) incorrectly we have committed a Type I error.

95% Confidence Interval

2.02771.9723