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Chapter 9: Q6CQQ (page 414)

True? Determine whether the following statement is true: When random samples of 50 men and 50 women are obtained, and we want to test the claim that men and women have different mean annual incomes, there is no need to confirm that the samples are from populations with normal distributions.

Short Answer

Expert verified

It is true that there is no need to confirm that the samples are from populations that are normally distributed.

Step by step solution

01

Given information

Random samples of 50 men and 50 women are obtained to test the claim that men and women have different mean annual incomes.

02

Normality requirement of t-test

In order to test the given claim, a t-test to check the equality of means for independent samples needs to be conducted.

The t-test requires one of the following two conditions to be met:

  • The populations from which the samples are taken are normally distributed.
  • The sample sizes of the two samples are greater than 30.

Here, the sample sizes are equal to 50 and hence, are greater than 30.

Hence there is no need to confirm that the samples are from populations with normal distribution as one of the above two requirements is fulfilled.

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