9-2 Two Means: Independent Samples 467 14. IQ and Lead Exposure Data Set 11 “IQ and Lead” in Appendix B lists full IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The statistics are summarized below. a. Use a 0.05 significance level to test the claim that the mean IQ score of people with low blood lead levels is higher than the mean IQ score of people with high blood lead levels. b. Construct a confidence interval appropriate for the hypothesis test in part (a). c. Does exposure to lead appear to have an effect on IQ scores? Low Blood Lead Level: n = 78, x = 92.88462, s = 15.34451 High Blood Lead Level: n = 21, x = 86.90476, s = 8.988352 15. Are Quarters Now Lighter? Weights of quarters are carefully considered in the design of the vending machines that we have all come to know and love. Data Set 40 “Coin Weights” in Appendix B includes weights of a sample of pre-1964 quarters (n = 40, x = 6.19267 g, s = 0.08700 g) and weights of a sample of post-1964 quarters (n = 40, x = 5.63930 g, s = 0.06194 g). a. Use a 0.05 significance level to test the claim that pre-1964 quarters have a mean weight that is greater than the mean weight of post-1964 quarters. b. Construct a confidence interval appropriate for the hypothesis test in part (a). c. Do post-1964 quarters appear to weigh less than before 1964? If so, why aren’t vending machines affected very much by the difference? 16. Bad Stuff in Children’s Movies Data Set 20 “Alcohol and Tobacco in Movies” in Appendix B includes lengths of times (seconds) of tobacco use shown in animated children’s movies. For the Disney movies, n = 33, x = 61.6 sec, s = 118.8 sec. For the other movies, n = 17, x = 49.3 sec, s = 69.3 sec. The sorted times for the non-Disney movies are listed below. a. Use a 0.05 significance level to test the claim that Disney animated children’s movies and other animated children’s movies have the same mean time showing tobacco use. b. Construct a confidence interval appropriate for the hypothesis test in part (a). c. Conduct a quick visual inspection of the listed times for the non-Disney movies and comment on the normality requirement. How does the normality of the 17 non-Disney times affect the results? 0 0 0 0 0 0 1 5 6 17 24 55 91 117 155 162 205 17. Are Weights Changing Over Time? Listed below are weights (kg) of randomly selected U.S. Army male personnel measured in 1988 (from Data Set 2 “ANSUR I 1988”) and different weights (kg) of randomly selected U.S. Army male personnel measured in 2012 (from Data Set 3 “ANSUR II 2012”). a. Use a 0.05 significance level to test the claim that the mean weight of the 1988 population is less than the mean weight of the 2012 population. b. Construct a confidence interval appropriate for the hypothesis test in part (a). ANSUR I 1988 76.985.297.969.4 71.277.778.275.684.472.060.683.0 ANSUR II 2012 79.2 91.5 96.5 67.5 107.3 79.3 78.2 88.2 71.5 94.7 66.5 87.9 67.5 88.4 69.5 18. Queues Listed on the next page are waiting times (seconds) of observed cars at a Delaware inspection station. The data from two waiting lines are real observations, and the data from the single waiting line are modeled from those real observations. These data are from Data Set 30 “Queues” in Appendix B. The data were collected by the author. continued
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