384 CHAPTER 7 Hypothesis Testing with One Sample Using and Interpreting Concepts Hypothesis Testing Using Rejection Regions In Exercises 19–26, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed. 19. Listening Time A product review claims that Apple AirPods have a mean listening time of at least 5.0 hours on a single charge. You suspect this claim is incorrect and find that a random sample of 18 pairs of AirPods has a mean single-charge listening time of 4.69 hours and a standard deviation of 0.57 hour. Is there enough evidence to reject the claim at a = 0.01? 20. DMV Wait Times A state Department of Transportation claims that the mean wait time for various services at its different locations is at most 6 minutes. A random sample of 34 services at different locations has a mean wait time of 10.3 minutes and a standard deviation of 8.0 minutes. Is there enough evidence to reject the claim at a = 0.01? 21. Credit Card Debt A credit reporting agency claims that the mean credit card debt in Colorado is greater than $5540 per borrower. You want to test this claim. You find that a random sample of 30 borrowers has a mean credit card debt of $5594 per person and a standard deviation of $597 per person. At a = 0.05, can you support the claim? (Adapted from Experian) 22. Used Car Cost A used car dealer says that the mean price of a three-year-old sport utility vehicle (in good condition) is $20,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $20,640 and a standard deviation of $1990. Is there enough evidence to reject the claim at a = 0.05? 23. Carbon Monoxide Levels As part of your work for an environmental awareness group, you want to test a claim that the mean amount of carbon monoxide in the air in U.S. cities is less than 1.80 parts per million. You find that the mean amount of carbon monoxide in the air for a random sample of 64 U.S. cities is 1.92 parts per million and the standard deviation is 1.39 parts per million. At a = 0.10, can you support the claim? (Adapted from U.S. Environmental Protection Agency) 24. Lead Levels As part of your work for an environmental awareness group, you want to test a claim that the mean amount of lead in the air in U.S. cities is less than 0.032 microgram per cubic meter. You find that the mean amount of lead in the air for a random sample of 56 U.S. cities is 0.021 microgram per cubic meter and the standard deviation is 0.034 microgram per cubic meter. At a = 0.01, can you support the claim? (Adapted from U.S. Environmental Protection Agency) 25. Annual Salary An employment information service claims the mean annual salary for mid-level product engineers is $86,000. The annual salaries (in dollars) for a random sample of 16 mid-level product engineers are shown in the table at the left. At a = 0.05, test the claim that the mean salary is $86,000. (Adapted from Salary.com) 26. Annual Salary An employment information service claims the mean annual salary for senior level statisticians is more than $124,000. The annual salaries (in dollars) for a random sample of 12 senior level statisticians are shown in the table at the left. At a = 0.10, is there enough evidence to support the claim that the mean salary is more than $124,000? (Adapted from Salary.com) Annual salaries 88,050 70,505 80,450 79,000 84,000 62,100 63,900 70,088 81,500 64,500 92,020 73,000 101,200 68,970 91,400 98,350 TABLE FOR EXERCISE 25 Annual salaries 126,200 136,000 129,200 109,800 137,500 118,000 116,500 130,000 130,400 133,500 137,000 148,300 TABLE FOR EXERCISE 26
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