392 CHAPTER 7 Hypothesis Testing with One Sample Hypothesis Testing Using a P-Value In Exercises 13–16, (a) identify the claim and state H0 and Ha, (b) use technology to find the P-value, (c) decide whether to reject or fail to reject the null hypothesis, and (d) interpret the decision in the context of the original claim. 13. Space Travel A research center claims that 27% of U.S. adults would travel into space on a commercial flight if they could afford it. In a random sample of 1000 U.S. adults, 30% say that they would travel into space on a commercial flight if they could afford it. At a = 0.05, is there enough evidence to reject the research center’s claim? (Source: Rasmussen Reports) 14. Meat and Poultry A research center claims that at most 35% of U.S. adults seek to buy naturally raised and fed meat and poultry. In a random sample of 1000 U.S. adults, 38% say they seek to buy naturally raised and fed meat and poultry. At a = 0.01, is there enough evidence to reject the center’s claim? (Source: FoodPrint) 15. Moral Values A politician claims that more than 25% of U.S. adults believe moral values in the country are getting better. In a random sample of 50 U.S. adults, 17 say moral values in the country are getting better. At a = 0.10, can you support the politician’s claim? (Adapted from Gallup) 16. Stray Cats An animal advocate claims that 25% of U.S. households have taken in a stray cat. In a random sample of 500 U.S. households, 105 say they have taken in a stray cat. At a = 0.05, is there enough evidence to reject the advocate’s claim? (Adapted from American Pet Products Association) Protecting the Environment In Exercises 17 and 18, use the figure at the left, which suggests what adults think about protecting the environment. (Adapted from Pew Research Center) 17. Are People Concerned About Protecting the Environment? You interview a random sample of 100 adults. The results of the survey show that 58% of the adults said they live in ways that help protect the environment some of the time. At a = 0.05, can you reject the claim that at least 64% of adults make an effort to live in ways that help protect the environment some of the time? 18. What Are People’s Attitudes About Protecting the Environment? Use your conclusion from Exercise 17 to write a paragraph on people’s attitudes about protecting the environment. Extending Concepts Alternative Formula In Exercises 19 and 20, use the information below. When you know the number of successes x, the sample size n, and the population proportion p, it can be easier to use the formula z = x - np 1 npq to find the standardized test statistic when using a z-test for a population proportion p. 19. Rework Exercise 7 using the alternative formula and verify that the results are the same. 20. The alternative formula is derived from the formula z = np - p 2 pq n = (x n) - p 2 pq n . Use this formula to derive the alternative formula. Justify each step. Protecting the Environment How often adults say they make an effort to live in ways that help protect the environment: Some of the time 64% Not too often/ Not at all 11% All of the time 25% FIGURE FOR EXERCISES 17 AND 18
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