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 pooled variance is used to estimate the standard error of the sampling distribution of the sample mean difference when the populations are normal with equal variances. When the sample sizes are large, the standard error can also be estimated using individual sample variances. When the populations are non-normal with unequal variances, a modification called the Welch's t-test is used. Therefore, option B is the best choice as it reflects the appropriate condition for using the pooled variance.

In Testing the Difference Between Two Population Means Using Two