patient pre post 1 3.7 3.7 2 4.6 4.4 3 4.9 3.8 4 4.8 4.1 5 4.1 4.8 6 3.9 3.8 7 4.1 5.8 8 4.5 4.8 9 5.2 4.3 10 3.6 4.5 11 4.1 4.5 12 3.6 5.8 13 3 5.1 14 4.8 6.1 15 4.6 3.3 16 3.6 5.5 17 3.6 4.9 18 3.2...

patient	pre	post
1	3.7	3.7
2	4.6	4.4
3	4.9	3.8
4	4.8	4.1
5	4.1	4.8
6	3.9	3.8
7	4.1	5.8
8	4.5	4.8
9	5.2	4.3
10	3.6	4.5
11	4.1	4.5
12	3.6	5.8
13	3	5.1
14	4.8	6.1
15	4.6	3.3
16	3.6	5.5
17	3.6	4.9
18	3.2	5.7
19	4.7	3.3
20	3.3	6.1

nvestigation of anti-body levels in a group of 22 patients before and after injection of an immunoglobulin produced the datasets provided in statexam2q5.csv . (a) Write a null and alternate hypothesis set to test if there is evidence for post-injection anti-body levels to be greater than pre-injection levels. (b) Test your hypothesis using the appropriate hypothesis test and significance level. (c) Compute a 99% confidence interval for the difference between pre and post-injection antibody levels. (d) Bonus: Assume you have strong reason to believe the assumption of normality is false in this case. Conduct an appropriate hypothesis test similar to a) and report your result.