In testing the difference between two population means using two independent samples,we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if:
A) the sample sizes are both large.
B) the populations are normal with equal variances.
C) the populations are non-normal with unequal variances.
D) All of these choices are true.

Question

In testing the difference between two population means using two independent samples,we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference  if:
A) the sample sizes are both large. 
B) the populations are normal with equal variances. 
C) the populations are non-normal with unequal variances. 
D) All of these choices are true.

Quizplus · Accepted Answer

The use of pooled variance in estimating the standard error of the sampling distribution of the sample mean difference is appropriate when the populations are normal with equal variances. This assumption is necessary for the validity of the t-test used to test the difference between two population means. If the populations are non-normal or the variances are unequal, alternative methods such as the Welch's t-test should be used. If the sample sizes are both large, the t-test can still be used even if the populations are not normal, but the use of pooled variance is not necessary.

In Testing the Difference Between Two Population Means Using Two