1 Chapter 12: Inference for Proportions 12.1Inference for a Population Proportion 12.2Comparing Two Proportions

2 Sampling Distribution of p-hat From Chapter 9: p-hat is an unbiased estimator of p. standard deviation of p-hat:

3 Figure 12.1, p. 687

4 Conditions for Inference about a Proportion (p. 687) SRS N at least 10n For a significance test of H 0 :p=p 0 : The sample size n is so large that both np 0 and n(1-p 0 ) are at least 10. For a confidence interval: n is so large that both the count of successes, n*p-hat, and the count of failures, n(1 - p-hat), are at least 10.

5 Can we make inferences about a proportion? Exercises 12.4 and 12.5, p. 689

6 Normal Sampling Distribution If these conditions are met, the distribution of p-hat is approximately normal, and we can use the z-statistic:

7 Inference for a Population Proportion Confidence Interval: Significance test of H 0 : p=p 0 :

8 Practice Exercise 12.7, p. 694

9 Homework Read all of 12.1 (pp ) Exercises: 12.14, 12.15, p. 698

10 Choosing a Sample Size (p. 695) Our guess p * can be from a pilot study, or we could use the most conservative guess of p * =0.5. Solve for n. Example 12.9, p. 696.

11 Practice Exercises: 12.10, p , p. 694

12 Homework Reading, Section 12.2: pp

Comparing Two Proportions

14 Conditions: Confidence Intervals for Comparing Two Proportions SRS from each population N>10n from each population All of these are at least 5:

15 Calculating a Confidence Interval for Comparing Two Proportions (p. 704) Two prop: Remember the one-prop formula:

16 Practice Problem 12.23, p. 706

17 Significance Tests for Comparing Two Proportions Example 12.12, p. 707 H 0 : p 1 =p 2 vs. H a : p 1 <p 2 “If H 0 is true, all observations in both samples really come from a single population of men of whom a single unknown proportion p will have a heart attack in a five-year period. So instead of estimating p 1 and p 2 separately, we pool the two samples and use the overall sample proportion to estimate the single population parameter p.

18 Significance Tests for Comparing Two Proportions The test statistic is: Where,

19 Conditions: Significance Test for Comparing Two Proportions SRS from each population N>10n from each population All of these are at least 5:

20 Practice Problem 12.25, p. 712

21 Practice Problems: 12.36, p , p , p. 721 Chapter 12 test on Monday Formulas provided: