Question

1. For the data below perform a Wilcoxon Rank-Sum Test by-hand showing all steps (you may verify your results using software if you want to but it’s not required).
   Two treatments were developed for asthma patients. Twelve patients were randomly assigned to one of Treatment A or Treatment B (six patients on each treatment). The response variable is the number of days that the patients were symptom free after using their assigned treatments for a week. Test to see if Treatment A has a distribution that is shifted to the right (i.e. tends to have larger values) than Treatment B.
   Show all steps of your test and use 5% level of significance.

Trt A	4	8	7	14	10	13
Trt B	2	11	9	3	15	6

Answer 1

Solution-

from the given data wilcoxon rank sum test is calculated-

test results-

So, the test results that the null hypothesis is not rejected.

Hence , there is not enough evidence to claim that the Treatment A has a distribution shifted to right (i.e. tends to have larger values) than treatment B