Do people of different age groups differ in their response to e-mail messages? A survey by the Center for the Digital Future of the University of Southern California reported that 70.7% of users over age 70 believe that e-mail messages should be answered quickly, as compared to 53.6% of users 12 to 50 years old. (Data extracted from A. Mindlin, "Older E-mail Users Favor Fast Replies," The New York Times, July 14, 2008, p. B3.) Suppose
that the survey was based on 1,000 users over age 70 and 1,000 users 12 to 50 years old.
a. At the 0.01 level of significance, is there evidence of a significant difference between the two age groups in their belief that e-mail messages should be answered quickly?
b. Find the p-value in (a) and interpret its meaning.