Chapter Test 411 Chapter Test 7 Take this test as you would take a test in class. 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 retail grocery chain owner claims that at least 25% of adults have purchased a meal kit in a recent year. In a random sample of 36 adults, 19% have purchased a meal kit in a recent year. At a = 0.10, is there enough evidence to reject the owner’s claim? (Adapted from PYMNTS) 2. A travel analyst claims that the mean of the room rates for two adults at three-star hotels in Salt Lake City is $134. In a random sample of 37 three-star hotels in Salt Lake City, the mean room rate for two adults is $143. Assume the population standard deviation is $30. At a = 0.10, is there enough evidence to reject the analyst’s claim? (Adapted from Expedia) 3. A travel analyst says that the mean price of a meal for a family of 4 in a resort restaurant is at most $100. A random sample of 33 meal prices for families of 4 has a mean of $110 and a standard deviation of $19. At a = 0.01, is there enough evidence to reject the analyst’s claim? 4. A research center claims that more than 80% of U.S. adults think that mothers should have paid maternity leave. In a random sample of 50 U.S. adults, 82% think that mothers should have paid maternity leave. At a = 0.05, is there enough evidence to support the center’s claim? (Adapted from Pew Research Center) 5. A nutrition bar manufacturer claims that the standard deviation of the number of grams of carbohydrates in a bar is 1.11 grams. A random sample of 26 bars has a standard deviation of 1.19 grams. At a = 0.05, is there enough evidence to reject the manufacturer’s claim? Assume the population is normally distributed. 6. A nonprofit consumer organization says that the mean rating of gas grills the organization rated in a recent year is less than 64. In a random sample of 50 gas grills the organization rated in a recent year, the mean rating is 62.9 and the standard deviation is 8.1. At a = 0.01, is there enough evidence to support the organization’s claim? (Adapted from Consumer Reports) 7. A researcher claims that the mean age of the residents of a small town is more than 38 years. The ages (in years) of a random sample of 30 residents are listed below. At a = 0.10, is there enough evidence to support the researcher’s claim? Assume the population standard deviation is 9 years. 41 44 40 30 29 46 42 53 21 29 43 46 39 35 33 42 35 43 35 24 21 29 24 25 85 56 82 87 72 31
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