A May 2011 Harris Interactive poll asked American adult women, “How often do you think women of your age, who have no special risk factors for breast cancer, should have a mammogram to check for breast cancer?” Fifty percent of women age 40 to 49 years and 56% of women age 50 years or older said annually (www.harrisinteractive.com/NewsRoom/PressReleases/tabid/446/ctl/ReadCustomDefault/mid/ 1506/ArticleId/769/Default.aspx). Suppose that these results were based on samples of 1055 women age 40 to 49 years and 1240 women age 50 years or older.
a. Let p1 and p2 be the proportions of all women age 40 to 49 years and age 50 years or older, respectively, who will say that women of their age with no special risk factors for breast cancer should have an annual mammogram. Construct a 98% confidence interval for p1  p2.
b. Using a 1% significance level, can you conclude that p1 is less than p2? Use both the critical-value and the p-value approaches.