SECTION 8.4 Testing the Difference Between Proportions 453 Daily Activities In Exercises 19–22, the results of a survey of 200 U.S. randomly selected U.S. men and 300 randomly selected U.S. women are shown in the figure at the left, which displays the percentages engaged in working or socializing and communicating on an average day. (Adapted from U.S. Bureau of Labor Statistics) 19. Men’s Activities At a = 0.01, can you support the claim that the proportion of men who work is greater than the proportion of men who socialize and communicate on an average day? 20. Women’s Activities At a = 0.01, can you reject the claim that the proportion of women who work is the same as the proportion of women who socialize and communicate on an average day? 21. Working At a = 0.01, can you support the claim that the proportion of women who work is less than the proportion of men who work on an average day? 22. Communicating At a = 0.10, can you support the claim that the proportion of women who socialize and communicate is greater than the proportion of men who socialize and communicate on an average day? Extending Concepts Constructing Confidence Intervals for p1 − p2 You can construct a confidence interval for the difference between two population proportions p1 - p2 by using the inequality below. 1np 1 - np 22 - zcBnp 1 nq 1 n1 + np 2 nq 2 n2 6 p1 - p2 6 1 np 1 - np 22 + zcBnp 1 nq 1 n1 + np 2 nq 2 n2 In Exercises 23–26, construct the indicated confidence interval for p1 - p2. Assume the samples are random and independent. 23. Students Planning to Study Visual and Performing Arts In a survey of 10,000 students taking the SAT, 7% were planning to study visual and performing arts in college. In another survey of 8000 students taken 10 years before, 8% were planning to study visual and performing arts in college. Construct a 95% confidence interval for p1 - p2, where p1 is the proportion from the recent survey and p2 is the proportion from the survey taken 10 years ago. (Adapted from College Board) 24. Students Undecided on an Intended College Major In a survey of 10,000 students taking the SAT, 9% were undecided on an intended college major. In another survey of 8000 students taken 10 years before, 7% were undecided on an intended college major. Construct a 90% confidence interval for p1 - p2, where p1 is the proportion from the recent survey and p2 is the proportion from the survey taken 10 years ago. (Adapted from College Board) 25. Critical Threats In Section 6.3, Exercises 27 and 28, let p1 be the proportion of the population of U.S. adults who see cyberterrorism as a critical threat to the country and let p2 be the proportion of the population of U.S. adults who see the spread of infectious diseases as a critical threat to the country. Construct a 95% confidence interval for p1 - p2. Compare your result with the result in Section 6.3, Exercise 27. 26. Critical Threats Repeat Exercise 25 but with a 99% confidence interval. Describe the likelihood that equal proportions of the population see cyberterrorism and the spread of infectious diseases as critical threats in the next 10 years. Daily Activities Percentage engaged in the activity on an average day. Women Working Socializing & communicating 49% 37% 33% 37% Men FIGURE FOR EXERCISES 19–22
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