7-3 Estimating a Population Standard Deviation or Variance 353 7. White Blood Counts of Women 99% confidence; n = 147, s = 1.96 11000 cells>mL2. 8. Heights of Men 99% confidence; n = 153, s = 7.10 cm. Finding Confidence Intervals. In Exercises 9–16, assume that each sample is a simple random sample obtained from a population with a normal distribution. 9. Body Temperature Data Set 5 “Body Temperatures” in Appendix B includes a sample of 106 body temperatures having a mean of 98.20°F and a standard deviation of 0.62°F (for day 2 at 12 AM). Construct a 95% confidence interval estimate of the standard deviation of the body temperatures for the entire population. 10. Atkins Weight Loss Program In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12 months, their mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb. Construct a 90% confidence interval estimate of the standard deviation of the weight loss for all such subjects. Does the confidence interval give us information about the effectiveness of the diet? 11. Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. After treatment with zopiclone, 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from “Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults,” by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population and construct a 98% confidence interval estimate of the standard deviation of the wake times for a population with zopiclone treatments. Does the result indicate whether the treatment is effective? 12. Garlic for Reducing Cholesterol In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg>dL) had a mean of 0.4 and a standard deviation of 21.0 (based on data from “Effect of Raw Garlic vs Commercial Garlic Supplements on Plasma Lipid Concentrations in Adults with Moderate Hypercholesterolemia,” by Gardner et al., Archives of Internal Medicine, Vol. 167). Construct a 98% confidence interval estimate of the standard deviation of the changes in LDL cholesterol after the garlic treatment. Does the result indicate whether the treatment is effective? 13. Heights of Female Soccer Players Listed below are the heights (in.) of players on the U.S. Women’s National Soccer Team (at the time of this writing). Use those heights as a sample of the heights of all professional women soccer players to construct a 95% confidence interval estimate of s. If we assume that the standard deviation of heights of the population of U.S. women is 2.9 in. (based on the data in Data Set 1 “Body Data”), what does the confidence interval suggest about this claim: The heights of women who are professional soccer players vary less than women in the general population? 67 67 70 61 67 69 69 66 69 66 64 68 68 71 72 67 69 65 66 64 67 67 67 14. Mint Specs Listed below are weights (grams) from a simple random sample of pennies produced after 1983 (from Data Set 40 “Coin Weights” in Appendix B). Construct a 95% confidence interval estimate of s for the population of such pennies. What does the confidence interval suggest about the U.S. Mint specifications that now require a standard deviation of 0.0230 g for weights of pennies? 2.5024 2.5298 2.4998 2.4823 2.5163 2.5222 2.4900 2.4907 2.5017 15. Professor Evaluation Scores Listed below are student evaluation scores of professors from Data Set 28 “Course Evaluations” in Appendix B. Construct a 95% confidence interval estimate of s for each of the two data sets. Does there appear to be a difference in variation? Female 4.4 3.4 4.8 2.9 4.4 4.9 3.5 3.7 3.4 4.8 Males 4.0 3.6 4.1 4.1 3.5 4.6 4.0 4.3 4.5 4.3
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