2. Two therapeutics are administered to 13 COVID-19 patients in a pilot study to compare differences in recovery times (measured in days). See the table below:

Therapeutic A (recovery time in days)	Therapeutic B (recovery time in days)
8.8	9.9
8.4	9.0
7.9	11.1
8.7	9.6
9.1	8.7
9.6	10.4
	9.5

a) Using an independent samples one-tailed t-test at an = 0.01 level of significance, determine whether Therapeutic A has a significantly shorter recovery time on average than Therapeutic B. Pool the variances. Be sure to clearly state the null and alternate hypotheses. [10 marks]

b) Using a Mann-Whitney two-tailed test at an = 0.01 level of significance, determine whether there is a significant difference between Therapeutic A and Therapeutic B in terms of recovery time. Be sure to clearly state the null and alternate hypotheses. [10 marks]