A study group at a high school has interviewed random samples of students at higher grades several times since 2010. Most recently, of the students who reported reading Encyclopedia Britannica, the percentage who reported that reading “to portray their image as studious”

is an important reason for borrowing such books from the library was 35.2% of 4690 women students and 59.5% of 5120 male students. For comparing men and women,

(a) Show that the standard error for the estimated difference between the corresponding population proportions equals 0.0098.

(b) Show that the 95% confidence interval for the difference is (0.22, 0.26). Interpret.