316 CHAPTER 6 Confidence Intervals 22. You research driving distances to work and find that the population standard deviation is 5.2 miles. Repeat Exercise 18 using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results. 23. You research prices of cell phones and find that the population mean is $431.61. In Exercise 19, does the t-value fall between -t0.95 and t0.95? 24. You research repair costs of mobile devices and find that the population mean is $89.56. In Exercise 20, does the t-value fall between -t0.95 and t0.95? Constructing a Confidence Interval In Exercises 25–28, use the data set to (a) find the sample mean, (b) find the sample standard deviation, and (c) construct a 99% confidence interval for the population mean. Assume the population is normally distributed. 25. SAT Scores The SAT scores of 12 randomly selected high school seniors 1130 1290 1010 1320 950 1250 1340 1100 1260 1180 1470 920 26. Grade Point Averages The grade point averages of 14 randomly selected college students 2.3 3.3 2.6 1.8 3.1 4.0 0.7 2.3 2.0 3.1 3.4 1.3 2.6 2.6 27. College Football The weekly time (in hours) spent weight lifting for 16 randomly selected college football players 7.4 5.8 7.3 7.0 8.9 9.4 8.3 9.3 6.9 7.5 9.0 5.8 5.5 8.6 9.3 3.8 28. Homework The weekly time spent (in hours) on homework for 18 randomly selected high school students 12.0 11.3 13.5 11.7 12.0 13.0 15.5 10.8 12.5 12.3 14.0 9.5 8.8 10.0 12.8 15.0 11.8 13.0 29. In Exercise 25, the population mean SAT score is 1051. Does the t-value fall between -t0.99 and t0.99? (Source: The College Board) 30. In Exercise 28, the population mean weekly time spent on homework by students is 7.8 hours. Does the t-value fall between -t0.99 and t0.99? Constructing a Confidence Interval In Exercises 31 and 32, use the data set to (a) find the sample mean, (b) find the sample standard deviation, and (c) construct a 98% confidence interval for the population mean. 31. Earnings The annual earnings (in dollars) of 32 randomly selected intermediate level life insurance underwriters (Adapted from Salary.com) 90,198 65,357 62,108 78,201 80,882 74,759 46,382 75,196 56,412 74,610 65,460 68,066 53,610 92,391 57,579 99,477 42,363 47,315 67,769 50,110 92,437 58,188 76,515 65,997 42,713 77,745 57,928 94,066 61,748 91,868 62,445 70,359 32. Earnings The annual earnings (in dollars) of 35 randomly selected senior magnetic resonance imaging (MRI) technologists (Adapted from Salary.com) 103,806 70,214 110,577 121,456 95,061 110,951 95,055 113,446 100,863 72,326 76,846 108,294 106,126 85,180 88,122 81,264 109,829 83,494 108,233 86,573 99,753 126,366 71,103 126,437 101,852 96,375 101,702 104,606 85,439 102,420 52,090 83,010 101,074 101,895 58,667
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