9-1 Two Proportions 453 19. Blue Eyes and Gender Professors collected data consisting of eye color and gender of statistics students. Among 1107 female students, 370 had blue eyes. Among 919 male students, 359 had blue eyes (based on data from “Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask,” by Froelich and Stephenson, Journal of Statistics Education, Vol. 21, No. 2). Use a 0.01 significance level to test the claim that the proportions of blue eyes are the same for females and males. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. What is the type of sampling used? Is it likely that the sample is biased? 20. Brown Eyes and Gender Professors collected data consisting of eye color and gender of statistics students. Among 1107 female students, 352 had brown eyes. Among 919 male students, 290 had brown eyes (based on data from “Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask,” by Froelich and Stephenson, Journal of Statistics Education, Vol. 21, No. 2). Use a 0.01 significance level to test the claim that the proportions of brown eyes are the same for females and males. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. What is the type of sampling used? Is it likely that the sample is biased? 21. Lefties In a random sample of males, it was found that 23 write with their left hands and 217 do not. In a random sample of females, it was found that 65 write with their left hands and 455 do not (based on data from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education Resources Information Center, Paper 399519). We want to use a 0.01 significance level to test the claim that the rate of left-handedness among males is less than that among females. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Based on the results, is the rate of left-handedness among males less than the rate of left-handedness among females? 22.Ground vs. Helicopter for Serious Injuries A study investigated rates of fatalities among patients with serious traumatic injuries. Among 61,909 patients transported by helicopter, 7813 died. Among 161,566 patients transported by ground services, 17,775 died (based on data from “Association Between Helicopter vs. Ground Emergency Medical Services and Survival for Adults With Major Trauma,” by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15). Use a 0.01 significance level to test the claim that the rate of fatalities is higher for patients transported by helicopter. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Considering the test results and the actual sample rates, is one mode of transportation better than the other? Are there other important factors to consider? 23.Determining Sample Size The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 - a can be found by using the following expression: E = za>2Ap1q1 n1 + p2q2 n2 9-1 Beyond the Basics continued
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