Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. For each part, decide whether you would use the pooled t-test, the nonpooled t-test, the Mann– Whitney test, or none of these tests.

Nannie Mack

Nannie Mack

Answered question

2021-08-10

Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. For each part, decide whether you would use the pooled t-test, the nonpooled t-test, the Mann– Whitney test, or none of these tests if preliminary data analyses of the samples suggest that the two distributions of the variable under consideration are a. normal but do not have the same shape. b. not normal but have the same shape. c. not normal and do not have the same shape. both sample sizes are large.

Answer & Explanation

Ian Adams

Ian Adams

Skilled2021-08-16Added 163 answers

Step 1 a).It is given that the distributions of the variables are normal but do not have the same shape. Hence, it is expected that the standard deviations of the variables are not equal. It is known that the pooled t-test can be used only when standard deviations of the variables are equal and the distributions are normal. Hence, it can be used non-pooled t test. Step 2 b).It is given that the distributions of the variables are not normal but have the same shape. Hence, it is expected that the standard deviations of the variables are equal. It is known that the pooled t-test can be used only when standard deviations of the variables are equal and the distributions are normal. Hence, it can be used Mann-Whitney test. Step 3 c).It is given that the distributions of the variables are not normal and also do not have the same shape. Hence, it is expected that the standard deviations of the variables are not equal. But the sample sizes of the samples are large. Hence by central limit theorem, it is expected that the populations are approximately normally distributed. It is known that the pooled t-test can be used only when standard deviations of the variables are equal and the distributions are normal. Hence, it can be used non-pooled t test.

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