# 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.

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.
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Step 1
From the provided information, the sample size for men is 50 and the sample size for women is also 50.
Step 2
According to the central limit theorem the sampling distribution of sample means approaches a normal distribution as the sample size gets larger. The sample sizes are large enough to be assumed as normally distributed. Therefore, there is no need to confirm that the samples are from population with normal distributions. Thus, the statement is true.