In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results: Table 1: Results of Smoking Survey Sample 1 Sample 2 E1 = 5275 :32 = 5240 $1 = 150 82 = 200 (a) Use a 95% condence interval to estimate the difference between the population means #1 #2- (b) Test the null hypothesis H0 : (pal M2) = 0 versus the alternative hypothesis Ha : (n1 M2) 75 0. Give the p-value of the test, and interpret the result. (c) Suppose the test in part (b) were conducted with the alternative hypothesis Ha : (,Lel #2) > 0. How would your answer to part (b) change? ((1) Test the null hypothesis H0 : (pal p.2) 2 25 versus the alternative Ha : (#1 ,ug) % 25. Give the pvalue, and interpret the result. Compare your answer with that obtained from the test conducted in part (b). (e) What assumptions are necessary to ensure the validity of the inferential procedures applied in parts (a)e(d)