4. A new medication is being developed to treat severe nausea and vomiting among chemotherapy patients. The information below was generated from a small sample size (n = 11) and shows the number of times a chemotherapy patient vomited both before and after treatment due to the side effects of chemotherapy. Set up and interpret the results of a sign test at the alpha equals .05 level to determine if there is a difference in symptoms before and after treatment.

Chemotherapy Patient	Before Treatment	After Treatment	Difference	Sign
1	9	3	6	+
2	12	5	8	+
3	14	7	7	+
4	9	4	5	+
5	8	2	6	+
6	11	3	8	+
7	15	7	8	+
8	12	8	4	+
9	7	8	-1	-
10	9	5	4	+
11	8	7	1	+

a. We reject H₀ in favor of H₁, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 1 is less or equal to the critical value 1 for a sign test with a population of only 11 individuals.

b. We reject H₀ in favor of H₁, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 10 is greater or equal to the critical value 1 for a sign test with a population of only 11 individuals.

c. We fail to reject H₀, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 1 is less or equal to critical value 1 for a sign test with a population of only 11 individuals.

d. We fail to reject H₀, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 10 is greater or equal to the critical value 1 for a sign test with a population of only 11 individuals.