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 normal with unequal variances
D) the populations are non-normal with unequal variances
E) all of these

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 normal with unequal variances 
D) the populations are non-normal with unequal variances 
E) all of these

Quizplus · Accepted Answer

When testing the difference between two population means with two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if the populations are normal with equal variances. This is because the pooled variance estimates the common variance of the two populations, allowing us to better estimate the standard error of the difference between means. If the populations are not normal or have unequal variances, we may need to use alternative methods such as the Welch's t-test. If the sample sizes are both large, we may be able to use the Central Limit Theorem to assume normality and estimate the standard error without pooling. However, this is not always reliable and it is generally safer to use the pooled variance when appropriate. Therefore, the best choice is B.

In Testing the Difference Between Two Population Means Using Two