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 $X _ { 1 } - X _ { 2 }$
if the populations are normal with equal variances.

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 $X _ { 1 } - X _ { 2 }$ 
if the populations are normal with equal variances.

Quizplus · Accepted Answer

The pooled variance is used when the populations are assumed to have equal variances, allowing for a more accurate estimate of the standard error in the sampling distribution of the difference between two means.

In Testing the Difference Between Two Population Means Using Two X1−X2X _ { 1 } - X _ { 2 }X1​−X2​

In Testing the Difference Between Two Population Means Using Two $X _ { 1 } - X _ { 2 }$