Question 1 [21 points]: A pharmaceutical research company in Mississauga is comparing the effectiveness of three different antihypertensive drugs. Each drug is administered to a group of eight patients over a period of three months to monitor the reduction in blood pressure. The decrease in systolic blood pressure (in mmHg) for each patient is recorded and presented in the following table. Assuming a 0.05 level of significance for your test:

Drug A	Drug B	Drug C
18.2	16.4	19.5
17.6	17	20.3
18.4	16.8	19.8
17.2	15.6	18.7
16.9	17.3	20.1
18	16.2	19.3
17.5	16.7	20.6
16.8	17.1	19

(a) Suggest an appropriate experimental design that should be employed for this study, considering its objectives and the nature of the data involved

(b) Calculate the mean and standard deviation for each data group

(c) Using StatCrunch, perform a statistical test to compare the mean blood pressure reduction across three treatments. At a significance level of = 0.05:

(1) Formulate hypotheses related to the differences in mean blood pressure reductions across the treatments

(2) Calculate and report the necessary statistical figures, including the test statistic, critical value, and p-value

(3) Make a decision and provide justification based on the analysis, employing both critical value and p-value methods

(d) Manually compute the pooled variance [1], and compare it to the Mean Squared Error (MSE) calculated from the ANOVA analysis in StatCrunch

(e) Where applicable, manually execute a multiple comparison procedure to identify significant mean differences among the groups at a significance level of = .05. In carrying out this procedure, you should

(1) Identify and calculate the total number of comparisons, the adjusted significance level, and the critical t-value

(2) Construct individual confidence intervals

(3) Interpret the results

(f) Regardless of the findings in part (d), manually conduct the Kruskal-Wallis test to determine whether there are variations in the distributions of blood pressure reduction efficacy among the three treatments. Complete the following steps:

(1) State the null and alternative hypotheses .

(2) Sort the data and assign ranks

(3) Calculate the test statistic, and determine the critical and p-values .

(4) Formulate well-supported conclusions based on the test's findings

(g) Perform the Kruskal Wallis test using StatCrunch and present the findings. Contrast these results with your manual analysis