Question: A study first reported in the Journal of the American Medical Association (7 December 1994) received wide spread attention as the first wide-scale study of the use of alcohol on American college campuses and was the subject of an article in Time magazine (19 December 1994, p. 16). The researchers surveyed 17,592 students at 140 four-year colleges in 40 states. One of the results they found was that about 8.8%, or about 1550 respondents, were frequent binge drinkers. They defined frequent binge drinking as having had at least four (for women) or five (for men) drinks at a single sitting at least three times during the previous 2 weeks.
a. Time magazine (19 December 1994, p. 66) reported that of the approximately 1550 frequent binge drinkers in this study, 22% reported having had unprotected sex. Find a 95% confidence interval for the true proportion of all frequent binge drinkers who had unprotected sex, and interpret the interval for someone who has no knowledge of statistics.
b. Notice that the results quoted in part a indicate that about 341 students out of the 17,592 interviewed said they were frequent binge drinkers and had unprotected sex. Compute a 95% confidence interval for the proportion of college students who are frequent binge drinkers and who also had unprotected sex.
c. Using the results from parts a and b, write two short news articles on the problem of binge drinking and unprotected sex. In one, make the situation sound as disastrous as you can. In the other, try to minimize the problem.