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3. A shoe manufacturer has developed a new running shoe that purportedly enables one to run faster. Eight adults participated in an experiment in which each ran a mile with regular track shoes and then ran a mile the next day with the new shoes. Their running times in seconds are below Runner Track Shoes New Shoes 1 321 318 2 307 299 3 397 401 4 269 260 5 285 285 6 364 363 7 295 289 8 302 296 Estimate the average difference in times between the track shoes and new shoes. Construct a 96% confidence interval. 5. Joseph Lister (for whom Listerine is named) was a British physician who was interested in the role of bacteria in human infections. He suspected that germs were involving in transmitting infection, and so he tried using carbolic acid as an operating room disinfectant. In 75 amputations, he used carbolic acid 40 times. Of the 40 amputations using carbolic acid, 34 patients lived. In the 35 amputations without carbolic acid, 19 lived. Construct a 95% confidence interval comparing the ratios of patients who survived between these groups. 6. In July 2002, the American Journal of Clinical Nutrition reported that 42% of 1546 African-American women studied had a vitamin D deficiency. The data came from a national nutrition study conducted by the Centers of Disease control in Atlanta. Conduct a 92% confidence interval for the fraction of African-American women who have a vitamin D deficiency. 8. In a study of how depression may impact one’s ability to survive a heart attack, the researchers reported the ages of the two groups they examined. The mean age of 2397 patients without cardiac disease was 69.8 years (SD=8.7 years), while for the 450 patients with cardiac disease the mean and standard deviation were 74.0 and 7.9 years, respectively. Create a 99% confidence interval for the difference in mean ages of the two groups.

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Estimate the average difference in times between the track shoes and new shoes. Construct a 96% confidence interval.

Matched pair t test
Ha: μd≠0

The differences are from 8 randomly chosen samples. N<15.

Differences in times are independent for each runner.n is small. So check if the differences are unimodal and roughly symmetric with no outliners.From the modified boxplot plotted on TI-83 calculator,there are no outliners. From its histogram it can be made out that the dataset of differences...

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