Problem 2. We have independent random samples drawn from normal distributions of the heights of adult males living in two countries: nx = 12, = 65.7 inches, sx = 4 inches and ny = 15, y = 68.2 inches, sy = 3 inches. [You don't have to simplify your answers for full credits.] (a) [4pts.] Find and approximate 98% confidence interval for the difference x - of the means of the populations of heights. Assume that , are unknown but = (b) [4pts.] Define a test statistic and a critical region for testing the null hypothesis Hoxy against the one-sided alternative hypothesis H px < y. Let a = 0.01. (c) [3pts.] Briefly explain how you define a test statistic for testing the null hypothesis Hoxy-3 against the one-sided alternative hypothesis H px> y - 3. :