SECTION 6.4 Confidence Intervals for Variance and Standard Deviation 335 18. Volleyball The numbers of service aces scored by 15 teams randomly selected from the top 50 NCAA Division I Women’s Volleyball teams for the 2021 season have a sample standard deviation of 26.1. Use an 80% level of confidence. (Source: National Collegiate Athletic Association) 19. Water Quality As part of a water quality survey, you test the water hardness in several randomly selected streams. The results are shown in the figure at the left. Use a 95% level of confidence. 20. Website Costs As part of a survey, you ask a random sample of business owners how much they would be willing to pay for a website for their company. The results are shown in the figure at the left. Use a 90% level of confidence. 21. Car Batteries The reserve capacities (in hours) of 18 randomly selected automotive batteries have a sample standard deviation of 0.25 hour. Use an 80% level of confidence. 22. Annual Precipitation The annual precipitation amounts (in inches) of a random sample of 61 years for Chicago, Illinois, have a sample standard deviation of 6.46. Use a 98% level of confidence. (Source: National Oceanic and Atmospheric Administration) 23. Drive-Thru Times The times (in seconds) spent by a random sample of 28 customers in the drive-thru of a fast-food restaurant have a sample standard deviation of 56.1. Use a 98% level of confidence. 24. Motorcycle Speeds The times (in seconds) to accelerate from 0 to 60 miles per hour for a random sample of 20 motorcycles have a sample standard deviation of 0.91. Use a 90% level of confidence. Extending Concepts 25. Bolt Diameters You are analyzing the sample of bolts in Exercise 13. The population standard deviation of the bolts’ diameters should be less than 0.5 inch. Does the confidence interval you constructed for s suggest that the variation in the bolts’ diameters is at an acceptable level? Explain your reasoning. 26. Drug Concentration You are analyzing the times for the drug concentrations to peak in the patients in Exercise 14. The population standard deviation of the times for epinephrine concentrations to peak should be less than 10 minutes. Does the confidence interval you constructed for s suggest that the variation in the times is at an acceptable level? Explain your reasoning. 27. Battery Reserve Capacities You are analyzing the sample of car batteries in Exercise 21. The population standard deviation of the batteries’ reserve capacities should be less than 0.25 hour. Does the confidence interval you constructed for s suggest that the variation in the batteries’ reserve capacities is at an acceptable level? Explain your reasoning. 28. Drive-Thru Times You are analyzing the sample of drive-thru times in Exercise 23. The population standard deviation of the drive-thru times should be less than 1 minute. Does the confidence interval you constructed for s suggest that the variation in the drive-thru times is at an acceptable level? Explain your reasoning. 29. In your own words, explain how finding a confidence interval for a population variance is different from finding a confidence interval for a population mean or proportion. Water quality survey n = 19 s = 15 grains/gallon FIGURE FOR EXERCISE 19 How much will you pay for your site? n = 30 s = $3600 FIGURE FOR EXERCISE 20
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