(1 point) In order to compare the means of two populations, independent random samples of 113 observations are selected from each population, with the following results: Sample 1 Sample 2 x1 = 5 X2 = 2 $1 = 165 $2 = 175 (a) Use a 96 % confidence interval to estimate the difference between the population means (HI - H2). S ( HI - H2) S (b) Test the null hypothesis: Ho : (#1 - #2) = 0 versus the alternative hypothesis: Ha : (M1 - #2) # 0. Using a = 0.04, give the following: () the test statistic z = (ii) the positive critical z score (iii) the negative critical z score The final conclusion is We can reject the null hypothesis (#1 - #2) = 0 in favor ofthe alternative (#1 - #2) # 0. O There is not sufficient evidence to reject the null hypothesis (#1 - #2) = 0. (c) Test the null hypothesis: Ho : (#1 - #2) = 25 versus the alternative hypothesis: Ha : (#1 - #2) # 25. Using a = 0.04, give the following: (i) the test statistic Z =(ii) the positive critical z score (ii) the negative critical z score The final conclusion is O We can reject the null hypothesis (#1 - #2) = 25 in favor of the alternative (#1 - /2) # 25. O There is not sufficient evidence to reject the null hypothesis (#1 - #2) = 25