Question

Alcohol abuse has been described by college presidents as the number one problem on campus and is an important cause of death in young adults. A survey of 17,096 students in U.S. four-year colleges collected information on drinking behavior and alcohol-related problems. The researchers defined “frequent binge-drinking” as having five or more drinks in a row three or more times in the past two weeks. According to their definition 3,314 students were classified as frequent5 binge-drinkers. Construct a 901% confidence interval around the true proportion of binge-drinkers.

Answer 1

(a) The sample size is n 17096 The number of subjects is X- 3314 The sample proportion is 3314 17096 0.193847 p0.19385 The best point estimate for p is p0.19385 1-0.193847 0.806153 0.806153 The standard error of the proportion is 0.193847 (1-0.193847) 17096 0.193847 (0.806153) 17096 0.15627 17096 0.0000091 0.003023365 SE- - 0.003023365 The 90.1% confidence interval for the around the true proportion of binge-drinkers is 0.193847-0.003023365) Sp s0.193847+o (0003023365) 0.19384700495 (0.003023365) Sp s0.193847+Z00495 (0.003023365) 0.193847-1.64972(0.003023365) Sp s0.193847 +1.64972(0.003023365) 0.193847 0.004987709 Sp S0.193847+0.004987709 0.188859 S p s0.198834 Interpretat on We can be 90.1% confident that the true proportion of binge-drinkers is between 0.1889 and 0.1988