Multiple sclerosis is a chronic disease that affects the central nervous system, which is the brain, spinal cord, and optic nerves. This can lead to a wide range of symptoms throughout the body. In a clinic trial of a new intervention for Multiple Sclerosis (MS), a group of 10 patients with MS are randomly assigned to the Treatment Group receiving the new treatment/intervention, while another group of 10 patients with MS on the waiting list are randomly assigned to the Control Group receiving no treatment/intervention. The memory scores recorded for these two groups are in the following table.

Treatment Group	Control Group
14	9
18	7
10	12
13	11
15	14
15	5
12	4
12	10
10	9
12	9

Assume the assumptions of normality are satisfied and population variances are equal. Do the data provide sufficient evidence at 5% level of significance that the treatment/intervention improves the memory performance? Assume that 1 and 2 designate the population average memory score of treatment and control group respectively.

a) Are the samples independent? Justify your answer.

b) Perform an appropriate parametric hypothesis test using critical value, p-value, and confidence interval approach at 5% level of significance stating all necessary steps (assumptions, hypotheses, decision zone, rejection rule, decision with justification).

c) You suspect the assumption of normality, so make a boxplot using STATCRUNCH/EXCEL to compare the distribution of memory scores of treatment and control group and include your output in the assignment. Comment on your findings about normality assumption. (STATCRUNCH/EXCEL)

d) Notwithstanding your answer to part (c), use an appropriate non-parametric test at 5% significance level to determine whether the treatment/intervention improves the memory performance using critical value approach. State the hypotheses clearly, show your manual calculation of ranks (EXCEL), test statistic, and decision. (Manual Calculation and EXCEL)

e) Use STATCRUNCH to perform the same non-parametric test done in part (d) using p-value approach. (STATCRUNCH)