Question

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?

Short answer

a). Yes, all the conditions are satisfied, the hypothesis test can be performed using a pooled $t-$test in the provided case.

b). No, the Mann-Whitney test is not appropriate for completing the hypothesis test in the current case.

c). Pooled$t-$test is a preferable method.

Step-by-step solution

Part (a) Step 1: Given Information

The standard deviations of independent samples from two populations of the variable under study are equal.

Part (a) Step 2: Explanation

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 investigation are regularly distributed and have equal standard deviations, according to the information provided.

Part (b) Step 1: Given Information

The standard deviations of independent samples from two populations of the variable under study are equal.

Part (b) Step 2: Explanation

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 investigation are regularly distributed and have equal standard deviations, according to the information provided.

Part (c) Step 1: Given Information

The standard deviations of independent samples from two populations of the variable under study are equal.

Part (c) Step 2: Explanation

From part (a) and (b) of this exercise, clearly pooled $t-$ test is preferable method.