Do people of different age groups differ in their beliefs about response time to email messages? A survey by the Center for the Digital Future of the University of Southern California reported that 70.7% of users over 70 years of age believe that email 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 NewYork Times, July 14, 2008, p. B3.) Suppose that the survey was based on 1,000 users over 70 years of age 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 the proportion that believe that email messages should be answered quickly?
b. Find the p-value in (a) and interpret its meaning.