2. Slide 2 - 25 Copyright © 2008 Pearson Education, Inc. Chapter 11 Inferences for Population Proportions

3. Slide 3 - 25 Copyright © 2008 Pearson Education, Inc. Definition 11.1

4. Slide 4 - 25 Copyright © 2008 Pearson Education, Inc. Formula 11.1

5. Slide 5 - 25 Copyright © 2008 Pearson Education, Inc. Key Fact 11.1

6. Slide 6 - 25 Copyright © 2008 Pearson Education, Inc. Example 11.2 Suppose that 19.1% of all U.S. employees play hooky; that is, that the population proportion is = 0.191. Then, according to Key Fact 11.1, for samples of size 1010, the variable is approximately normally distributed with mean = p = 0.191 and standard deviation Use simulation to make that fact plausible.

7. Slide 7 - 25 Copyright © 2008 Pearson Education, Inc. Solution Example 11.2 We first simulated 2000 samples of 1010 U.S. employees each. Then, for each of those 2000 samples, we determined the sample proportion,, of those who play hooky. Output 11.1 shows a histogram of those 2000 values of, which is shaped like the superimposed normal curve with parameters 0.191 and 0.012. Output 11.1

8. Slide 8 - 25 Copyright © 2008 Pearson Education, Inc. Procedure 11.1

9. Slide 9 - 25 Copyright © 2008 Pearson Education, Inc. Definition 11.2

10. Slide 10 - 25 Copyright © 2008 Pearson Education, Inc. Formula 11.2

11. Slide 11 - 25 Copyright © 2008 Pearson Education, Inc. Procedure 11.2

12. Slide 12 - 25 Copyright © 2008 Pearson Education, Inc. Procedure 11.2 (cont.)

13. Slide 13 - 25 Copyright © 2008 Pearson Education, Inc. Key Fact 11.2

14. Slide 14 - 25 Copyright © 2008 Pearson Education, Inc. Procedure 11.3

15. Slide 15 - 25 Copyright © 2008 Pearson Education, Inc. Procedure 11.3 (cont.)

16. Slide 16 - 25 Copyright © 2008 Pearson Education, Inc. Example 11.9 Zogby International surveyed 1181 U.S. adults to gauge the demand for vegetarian meals in restaurants. The study, commissioned by the Vegetarian Resource Group and published in the Vegetarian Journal, polled independent random samples of 747 men and 434 women. Of those sampled, 276 men and 195 women said that they sometimes order a dish without meat, fish, or fowl when they eat out. Do the data from the Zogby International poll provide sufficient evidence to conclude that the percentage of U.S. men who sometimes order veg is smaller than the percentage of U.S. women who sometimes order veg? Use a 5% level of significance.

17. Slide 17 - 25 Copyright © 2008 Pearson Education, Inc. Solution Example 11.9 We apply Procedure 11.3, noting first that the assumptions for its use are satisfied. STEP 1 State the null and alternative hypotheses. Let p 1 and p 2 denote the proportions of all U.S. men and all U.S. women who sometimes order veg, respectively. The null and alternative hypotheses are H 0 : p 1 = p 2 (percentage for men is not less than that for women) H a : p 1 < p 2 (percentage for men is less than that for women). STEP 2 Decide on the significance level, α. The test is to be performed at the 5% significance level, or α = 0.05.

18. Slide 18 - 25 Copyright © 2008 Pearson Education, Inc. Solution Example 11.9 STEP 3 Compute the value of the test statistic where We first obtain,, and. Because 276 of the 747 men sampled and 195 of the 434 women sampled sometimes order veg, x 1 = 276, n 1 = 747, x 2 = 195, and n 2 = 434. Therefore,

19. Slide 19 - 25 Copyright © 2008 Pearson Education, Inc. Solution Example 11.9 and Consequently, the value of the test statistic is

20. Slide 20 - 25 Copyright © 2008 Pearson Education, Inc. Solution Example 11.9 OR

21. Slide 21 - 25 Copyright © 2008 Pearson Education, Inc. Solution Example 11.9 OR

22. Slide 22 - 25 Copyright © 2008 Pearson Education, Inc. Solution Example 11.9

23. Slide 23 - 25 Copyright © 2008 Pearson Education, Inc. Solution Example 11.9 STEP 6 Interpret the results of the hypothesis test. Interpretation At the 5% significance level, the data provide sufficient evidence to conclude that, in the United States, the percentage of men who sometimes order veg is smaller than the percentage of women who sometimes order veg.

24. Slide 24 - 25 Copyright © 2008 Pearson Education, Inc. Procedure 11.4

25. Slide 25 - 25 Copyright © 2008 Pearson Education, Inc. Formula 11.3

26. Slide 26 - 25 Copyright © 2008 Pearson Education, Inc. Formula 11.4