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 of the variable under consideration have the same shape, but are not normal, and both sample sizes are large. 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?

Independent samples from two populations of the same variable have the same shape, but they are not normal, and both samples are huge.

For comparing two population means, the following assumptions are made when using the pooled $t$ - test and pooled $t$ - interval test.

1.) Random variables that are easy to understand

2.) Samples from different people

3) A large sample or a normal population.

4.) The population standard deviation is the same.

Independent samples from two populations of the variable under examination have the same shape but are not normal, and both samples are large, according to the information provided.

There is no way of knowing if the sample standard deviations of two populations are comparable or equal. If assumption $4$ is true, then the hypothesis test can be performed using a pooled $t-$ test in the provided case.

Independent samples from two populations of the same variable have the same shape, but they are not normal, and both samples are huge.

A nonparametric approach is used to compare the means of two populations when the samples are not normal and the samples are not huge.

The Mann-Whitney test is a nonparametric test that is employed when samples are independent and the two sample distributions of the variable under consideration (one from each population) have the same shape.

Independent samples from two populations of the variable under examination have the same shape, but are not normal, and both samples are large, according to the information provided.

Independent samples from two populations of the same variable have the same shape, but they are not normal, and both samples are huge.

From part, a and b of this exercise, clearly Mann-Whitney test is the preferable method.