The College Alcohol Study at the Harvard School of Public Health has interviewed random samples of students at four-year colleges several times since 1993. In the most recent study, of the students who reported drinking alcohol, the percentage who reported that drinking “to get drunk” is an important reason for drinking was 42.4% of 5123 women students and 55.2% of 3660 male students.

For comparing men and women,

(a) Show that the standard error for the estimated difference between the corresponding population proportions equals 0.0107.

(b) Show that the 95% confidence interval for the difference is (0.11, 0.15). Interpret.