8-3 Testing a Claim About a Mean 415 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 test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 min. Does zopiclone appear to be effective? 21. Lead in Medicine Listed below are the lead concentrations (in mg>g) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States (based on data from “Lead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet,” by Saper et al., Journal of the American Medical Association, Vol. 300, No. 8). Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 mg>g. 3.0 6.5 6.0 5.5 20.5 7.5 12.0 20.5 11.5 17.5 22. Got a Minute? Students of the author estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.05 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute? 69 81 39 65 42 21 60 63 66 48 64 70 96 91 65 23. Cell Phone Radiation Listed below are the measured radiation levels (in W>kg) corresponding to these cell phones: iPhone X, iPhone 7, Google Pixel, Samsung Galaxy S8, OnePlus 5, Motorola VE465, LG G3, and HTC Desire 310. The data are from the Federal Communications Commission. The Federal Communications Commission (FCC) has a standard that a cell phone radiation level must be 1.6 W>kg or less. Use a 0.01 significance level to test the claim that the sample is from a population of cell phones with a mean amount of radiation that is less than the FCC standard of 1.6 W>kg. 0.97 1.38 0.93 1.52 1.37 1.09 0.48 0.65 24. Dollar Coins Listed below are weights (grams) of dollar coins from Data Set 40 “Coin Weights” in Appendix B. Use a 0.01 significance level to test the claim that the sample is from a population with a mean equal to 8.1 grams, which is the weight specified by the mint. What is a reasonable explanation for the result? 8.1008 8.1072 8.0271 8.0813 8.0241 8.0510 7.9817 8.0954 8.0658 8.1238 8.1281 8.0307 8.0719 8.0345 8.0775 8.1384 8.1041 8.0894 8.0538 8.0342 Large Data Sets from Appendix B. In Exercises 25–28, use the data set from Appendix B to test the given claim. Use the P-value method unless your instructor specifies otherwise. 25. Los Angeles Commute Time Use the 1000 Los Angeles Commute times listed in Data Set 31 “Commute Times” to test the claim that the mean Los Angeles commute time is less than 35 minutes. Use a 0.01 significance level. Compare the sample mean to the claimed mean of 35 minutes. Is the difference between those two values statistically significant? Does the difference between those two values appear to have practical significance? 26. Taxi Fares Repeat Exercise 16 using all 703 of the New York City taxi fares listed in Data Set 32 “Taxis” from Appendix B. 27. Arm Span Use the arm span distances (mm) of the 4082 males listed in Data Set 3 “ANSUR II 2012” in Appendix B to test the claim that the sample is from a population with a mean less than 1818 mm. Use a 0.01 significance level. Compare the sample mean to the claimed mean of 1818 mm. Is the difference between those two values statistically significant? Does the difference between those two values appear to have practical significance? 28. Army Height Based on the results of the 1988 survey of U.S. Army personnel, the mean height of males is 1755.8 mm. Use the heights (mm) of the 4082 males listed in Data Set 3 “ANSUR II 2012” in Appendix B to test the claim that this sample collected in 2012 is from a population with a mean greater than 1755.8 mm. Use a 0.05 significance level. Does it appear that male army personnel were taller in 2012 than in 1988?
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