Following the initial study on the efficacy of three different antihypertensive drugs, the Mississauga-based pharmaceutical research company is now extending its research to understand the differential effects of these drugs based on patient gender. The study aims to compare the reduction in blood pressure across male and female patients.

	Drug A - BP Reduction	Drug B - BP Reduction	C - BP Reduction
Male	18	16.5	19.6
17.5	17.1	20.4
18.3	16.9	19.9
17.1	15.7	18.8
16.7	17.2	20.2
17.9	16.3	19.4
17.4	16.8	20.7
16.9	17	19.1
Female	18.3	16.3	19.4
17.7	16.9	20.1
18.5	16.6	19.6
17.3	15.5	18.5
17	17.4	20
18.1	16.1	19.1
17.6	16.6	20.4
17	17.3	18.9

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

(b) Investigate the potential interaction effect between the type of drug and gender on blood pressure reduction. Use StatCrunch for this analysis. Ensure your analysis includes:

(1) Formulation of hypotheses that specifically address the interaction between the type of drug and gender .

2) Calculation and reporting of the necessary statistical values, including test statistic, critical value, and p-value.

(3) A decision based on your findings, supported by justifications using both critical value and p-value considerations

(c) Examine if significant differences in blood pressure reduction exist between male and female patients. Perform this analysis using StatCrunch, adhering to a 0.05 level of significance. Your analysis should comprise:

(1) Hypotheses focusing on the differences between genders.

2) Computation and reporting of the test statistic, critical value, and p-value relevant to gender comparison.

(3) A decision derived from your findings, along with justifications employing both critical value and p-value approaches

(d) Assess whether there are significant differences in average blood pressure reductions across the three drug types. Use StatCrunch for this analysis, maintaining a 0.05 level of significance. Include in your analysis:

(1) Hypotheses pertaining to the comparison of the three drug types

(2) Calculation and reporting of the test statistic, critical value, and p-value for this comparison

(3) A decision based on the analysis, supported by justifications using both critical value and p-value methods

(e) Manually calculate the 95% Bonferroni-adjusted margin of error for confidence intervals, focusing on all pairwise differences between the mean blood pressure reductions. Begin by identifying the total number of comparisons to determine the adjusted significance level. Then, calculate the critical t-value and use it to determine the adjusted margin of error. Next, assess whether significant differences exist in the following comparisons, and interpret the results:

(i) Between male and female patients for Drug B

(ii) Between Drug A and Drug C in female patients