Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions (one for each population) of the variable under consideration are normally distributed and have equal standard deviations. Answer the following questions and explain your answers.
a. Is it permissible to use the pooled t-test to perform the hypothesis test?
b. Is it permissible to use the Mann-Whitney test to perform the hypothesis test?
c. Which procedure is preferable, the pooled t-test or the Mann- Whitney test?