Review Exercises 407 In Exercises 25 and 26, (a) identify the claim and state H0 and Ha, (b) find the standardized test statistic z, (c) find the corresponding P-value, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. 25. A researcher claims that the mean air concentration of nitrogen dioxide in U.S. cities is 9 parts per billion (ppb). In a random sample of 52 U.S. cities, the mean air concentration of nitrogen dioxide is 8.1 ppb. Assume the population standard deviation is 5.65 ppb. At a = 0.05, can you reject the claim? (Source: U.S. Environmental Protection Agency) 26. A researcher claims that the mean air concentration of fine particulate matter (PM 2.5) in U.S. cities is greater than 9 micrograms per cubic meter 1mg m32. In a random sample of 84 U.S. cities, the mean air concentration of PM 2.5 is 8.25 mg m3. Assume the population standard deviation is 2.53 mg m3. At a = 0.01, can you support the claim? (Source: U.S. Environmental Protection Agency) In Exercises 27 and 28, (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 z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. 27. A substance abuse counselor claims that the mean annual drug overdose death rate for the 50 states is at least 25 deaths per 100,000 people. In a random sample of 30 states, the mean annual drug overdose rate is 22.48 per 100,000 people. Assume the population standard deviation is 10.69 deaths per 100,000. At a = 0.01, is there enough evidence to reject the claim? (Source: Centers for Disease Control and Prevention) 28. A travel analyst claims that the mean price of a round trip flight from New York City to Los Angeles is less than $725. In a random sample of 47 round trip flights from New York City to Los Angeles, the mean price is $712. Assume the population standard deviation is $133. At a = 0.05, is there enough evidence to support the travel analyst’s claim? (Adapted from Expedia) Section 7.3 In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance a and sample size n. 29. Two-tailed test, a = 0.05, n = 20 30. Right-tailed test, a = 0.01, n = 33 31. Right-tailed test, a = 0.02, n = 63 32. Left-tailed test, a = 0.05, n = 48 33. Left-tailed test, a = 0.005, n = 15 34. Two-tailed test, a = 0.02, n = 12 In Exercises 35–40, test the claim about the population mean m at the level of significance a. Assume the population is normally distributed. 35. Claim: m 7 12,700; a = 0.005. Sample statistics: x = 12,855, s = 248, n = 21 36. Claim: m Ú 0; a = 0.10. Sample statistics: x = -0.45, s = 2.38, n = 31 37. Claim: m … 51; a = 0.01. Sample statistics: x = 52, s = 2.5, n = 40 38. Claim: m 6 850; a = 0.025. Sample statistics: x = 875, s = 25, n = 14 39. Claim: m = 195; a = 0.10. Sample statistics: x = 190, s = 36, n = 101 40. Claim: m ≠ 333; a = 0.05. Sample statistics: x = 328, s = 13, n = 35
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