7 Chapter Quiz 410 CHAPTER 7 Hypothesis Testing with One Sample Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book. For each exercise, perform the steps below. (a) Identify the claim and state H0 and Ha. (b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning. (c) Choose one of the options. Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic. Option 2: Find the appropriate standardized test statistic and the P-value. (d) Decide whether to reject or fail to reject the null hypothesis. (e) Interpret the decision in the context of the original claim. 1. A hat company claims that the mean hat size for a male is at least 7.25. A random sample of 12 hat sizes has a mean of 7.15. At a = 0.01, can you reject the company’s claim? Assume the population is normally distributed and the population standard deviation is 0.27. 2. A travel analyst claims the mean daily base price for renting a full-size or less expensive vehicle in Vancouver, British Columbia, is more than $86. You want to test this claim. In a random sample of 40 full-size or less expensive vehicles available to rent in Vancouver, British Columbia, the mean daily base price is $93.23. Assume the population standard deviation is $28.90. At a = 0.10, do you have enough evidence to support the analyst’s claim? (Adapted from Expedia) 3. A government agency reports that the mean amount of earnings for full-time workers ages 18 to 24 with a bachelor’s degree in a recent year is $52,133. In a random sample of 15 full-time workers ages 18 to 24 with a bachelor’s degree, the mean amount of earnings is $48,400 and the standard deviation is $6679. At a = 0.05, is there enough evidence to reject the claim? Assume the population is normally distributed. (Adapted from U.S. Census Bureau) 4. A weight loss program claims that program participants have a mean weight loss of at least 10.5 pounds after 1 month. The weight losses after 1 month (in pounds) of a random sample of 40 program participants are listed below. At a = 0.01, is there enough evidence to reject the program’s claim? 4.7 6.0 7.2 8.3 9.2 10.1 14.0 11.7 12.8 10.8 11.0 7.2 8.0 4.7 11.8 10.7 6.1 8.8 7.7 8.5 9.5 10.2 5.6 6.9 7.9 8.6 10.5 9.6 5.7 9.6 12.6 12.9 6.8 12.0 5.1 14.0 9.7 10.8 9.1 12.9 5. A nonprofit consumer organization says that less than 25% of the televisions the organization rated in a recent year have an overall score of 70 or more. In a random sample of 35 televisions the organization rated in a recent year, 23% have an overall score of 70 or more. At a = 0.05, can you support the organization’s claim? (Adapted from Consumer Reports) 6. In Exercise 5, the nonprofit consumer organization says that the standard deviation of the television rating scores is 10.1. A random sample of 35 television rating scores has a standard deviation of 10.9. At a = 0.10, is there enough evidence to reject the organization’s claim? Assume the population is normally distributed. (Adapted from Consumer Reports)
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