376 CHAPTER 7 Hypothesis Testing with One Sample Hypothesis Testing Using Rejection Region(s) In Exercises 39– 44, (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. 39. Caffeine Content A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty-six 12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.4 milligrams. Assume the population standard deviation is 10.8 milligrams. At a = 0.01, can you reject the research organization’s claim? (Source: National Soft Drink Association) 40. High School Graduation Rate An education researcher claims that the mean high school 4-year graduation rate per state in the United States is 83%. You want to test this claim. You find that a random sample of 30 states has a mean high school 4-year graduation rate of 85%. Assume the population standard deviation is 3.9%. At a = 0.05, do you have enough evidence to reject the researcher’s claim? (Source: U.S. Department of Education) 41. Fast Food A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is less than 920 milligrams. A random sample of 40 breakfast sandwiches has a mean sodium content of 925 milligrams. Assume the population standard deviation is 18 milligrams. At a = 0.05, do you have enough evidence to support the restaurant’s claim? 42. Light Bulbs A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 750 hours. A random sample of 25 light bulbs has a mean life of 745 hours. Assume the population is normally distributed and the population standard deviation is 60 hours. At a = 0.02, do you have enough evidence to reject the manufacturer’s claim? 43. Fluorescent Lamps A compact fluorescent lamp (CFL) bulb manufacturer guarantees that the mean life of a CFL bulb is at least 10,000 hours. You want to test this guarantee. To do so, you record the lives of a random sample of 32 CFL bulbs. The results (in hours) are listed. Assume the population standard deviation is 1850 hours. At a = 0.11, do you have enough evidence to reject the manufacturer’s claim? 8,800 9,155 13,001 10,250 10,002 11,413 8,234 10,402 10,016 8,015 6,110 11,005 11,555 9,254 6,991 12,006 10,420 8,302 8,151 10,980 10,186 10,003 8,814 11,445 6,277 8,632 7,265 10,584 9,397 11,987 7,556 10,380 44. Gross Domestic Product A politician estimates that the mean gross domestic product (GDP) per country in a recent year is greater than $400 billion. You want to test this estimate. To do so, you determine the GDPs of 42 randomly selected countries for that year. The results (in billions of dollars) are shown in the table at the left. Assume the population standard deviation is $2099 billion. At a = 0.06, can you support the politician’s estimate? (Source: International Monetary Fund) Extending Concepts 45. Writing When P 7 a, does the standardized test statistic lie inside or outside of the rejection region(s)? Explain your reasoning. 46. Writing In a right-tailed test where P 6 a, does the standardized test statistic lie to the left or the right of the critical value? Explain your reasoning. Gross domestic product (in billions of dollars) 11 101 59 24 66 1883 403 11 18 61 50 3050 1.7 61 22 25 3.4 17 2.5 85 4.6 330 7.3 19 482 44 3.7 38 4.6 66 127 43 43 17 402 1618 151 16 24 14 7.8 300 TABLE FOR EXERCISE 44
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