376 Chapter 8 Confidence Intervals 12.23 12.32 11.87 12.34 11.48 12.66 8.51 14.13 12.95 10.30 9.34 8.63 a. Construct a 98% confidence interval for the mean weight of two-month-old baby girls. (9.986, 12.808) b. According to the National Health Statistics Reports, the mean weight of two-month-old baby boys is 11.5 pounds. Based on the confidence interval, is it reasonable to believe that the mean weight of two-month-old baby girls may be the same as that of two-month-old baby boys? Explain. Yes 30. Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 12 boxes: It is reasonable to assume that the population is approximately normal. 14.02 13.97 14.11 14.12 14.10 14.02 14.15 13.97 14.05 14.04 14.11 14.12 a. Construct a 98% confidence interval for the mean weight. (14.017, 14.113) b. The quality control manager is concerned that the mean weight is actually less than 14 ounces. Based on the confidence interval, is there a reason to be concerned? Explain. No 31. Eat your spinach: Six measurements were made of the mineral content (in percent) of spinach, with the following results. It is reasonable to assume that the population is approximately normal. 19.1 20.8 20.8 21.4 20.5 19.7 a. Construct a 95% confidence interval for the mean mineral content. (19.50, 21.26) b. Based on the confidence interval, is it reasonable to believe that the mean mineral content of spinach may be greater than 21%? Explain. Yes Source: Journal of Nutrition 66:55–66 32. Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia on June 20, 2013. It is reasonable to assume that the population is approximately normal. 4.750 4.375 4.176 4.679 4.426 4.227 4.125 4.250 3.950 4.191 4.299 4.415 Source: www.bankrate.com a. Construct a 99% confidence interval for the mean rate. (4.1190, 4.5428) b. One week earlier, the mean rate was 4.050%. A mortgage broker claims that the mean rate is now higher. Based on the confidence interval, is this a reasonable claim? Explain. Yes 33. Hi-def: Following are prices of a random sample of 18 smart TVs sold on shopper.cnet.com in 2013 with screen sizes between 46’’ and 50’’, along with a dotplot of the data. 548 598 697 699 749 799 829 849 928 1050 1098 1169 1198 1269 1299 1399 1455 1599 400 800 1200 1600 a. Is it reasonable to assume that the conditions for constructing a confidence interval for the mean price are satisfied? Explain. Yes b. If appropriate, construct a 95% confidence interval for the mean price of all smart TVs in this size range. (856.9, 1168.9) 34. Big salary for the boss: Following is the total 2012 compensation, in millions of dollars, for Chief Executive Officers at 20 large U.S. corporations, along with a boxplot of the data. 2.75 9.15 2.32 23.84 13.12 9.91 6.39 2.19 4.28 0.70 3.18 8.20 1.68 4.64 6.05 6.59 11.31 1.35 25.84 2.85 0 5 10 15 20 25 30 a. Is it reasonable to assume that the conditions for constructing a confidence interval for the mean compensation are satisfied? Explain. No b. If appropriate, construct a 95% confidence interval for the mean compensation of a Chief Executive Officer. Not appropriate 35. Pain relief: One of the ways in which doctors try to determine how long a single dose of pain-reliever will provide relief is to measure the drug’s half-life, which is the length of time it takes for one-half of the dose to be eliminated from the body. Following are half-lives (in hours) of the pain reliever oxycodone for a sample of 18 individuals, along with a boxplot of the data, based on a report of the National Institutes of Health. 3.3 1.7 2.0 5.0 1.2 2.8 3.7 3.5 4.8 4.7 4.9 2.5 5.1 6.0 3.9 4.3 2.1 3.0 1 2 3 4 5 6 a. Is it reasonable to assume that the conditions for constructing a confidence interval for the mean half-life are satisfied? Explain. Yes b. If appropriate, construct a 95% confidence interval for the mean half-life. (2.91, 4.26) c. The National Institutes of Health report states that the mean half-life is 3.51 hours. If appropriate, explain whether this confidence interval contradicts this claim. Does not contradict 36. How’s your mileage? Gas mileage, in miles per gallon, was measured for five 2012 Ford Explorer SUVs. Following are the results, along with a dotplot of the data. 20.4 19.6 17.1 17.9 18.7 17 17.5 18 18.5 19 19.5 20 20.5 21 a. Is it reasonable to assume that the conditions for constructing a confidence interval for the mean gas mileage are satisfied? Explain. Yes b. If appropriate, construct a 95% confidence interval for the mean gas mileage. (17.11, 20.37)
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