SECTION 6.2 Confidence Intervals for the Mean (s Unknown) 317 33. In Exercise 31, the population mean salary is $67,319. Does the t-value fall between -t0.98 and t0.98? (Source: Salary.com) 34. In Exercise 32, the population mean salary is $93,867. Does the t-value fall between -t0.98 and t0.98? (Source: Salary.com) Choosing a Distribution In Exercises 35–40, use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. 35. Body Mass Index In a random sample of 50 people, the mean body mass index (BMI) was 27.7 and the standard deviation was 6.12. 36. Mortgages In a random sample of 18 months from January 2011 through December 2020, the mean interest rate for 30-year fixed rate home mortgages was 3.95% and the standard deviation was 0.49%. Assume the interest rates are normally distributed. (Source: Freddie Mac) 37. Toddler Weights The population standard deviation of the weights of the two-year-old males on a pediatrician’s patient list is 2.49 pounds. The mean weight of a sample of 10 of the two-year-old males is 13.68 pounds. Weights are known to be normally distributed. 38. Data Use The mean number of gigabytes (GB) of data used in the past month by a sample of 18 college students is 7.9 GB with a standard deviation of 1.7 GB. The distribution is not symmetric due to the various limits on data plans. 39. Gas Mileage The gas mileages (in miles per gallon) of 28 randomly selected sports cars are listed. The mileages are not normally distributed. 21 30 19 20 21 24 18 24 27 20 22 30 25 26 22 17 21 24 22 20 24 21 20 18 20 21 20 27 40. Yards per Carry In the 2020–2021 NFL season, the population standard deviation of the yards per carry for all running backs was 1.76. The yards per carry of 13 randomly selected running backs are listed below. Assume the yards per carry are normally distributed. (Source: National Football League) 3.3 5.6 5.3 5.1 3.3 5.0 3.9 4.6 4.3 5.3 3.1 4.7 3.6 Extending Concepts 41. Tennis Ball Manufacturing A company manufactures tennis balls. When the balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean bounce height to be 55.5 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t@value falls between -t0.99 and t0.99, then the company will be satisfied that it is manufacturing acceptable tennis balls. For a random sample, the mean bounce height of the sample is 56.0 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Explain. 42. Light Bulb Manufacturing A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 1000 hours. This average is maintained by periodically testing random samples of 16 light bulbs. If the t@value falls between -t0.99 and t0.99, then the company will be satisfied that it is manufacturing acceptable light bulbs. For a random sample, the mean life span of the sample is 1015 hours and the standard deviation is 25 hours. Assume the life spans are approximately normally distributed. Is the company making acceptable light bulbs? Explain.
RkJQdWJsaXNoZXIy NjM5ODQ=