In developing confidence interval for the difference between two population means using two independent samples,we use the pooled estimate $s _ { p }$
in estimating the standard error of the sampling distribution of the sample mean difference $\bar { x } _ { 1 } - \bar { x } _ { 2 }$
if the populations are normal with equal variances.

Question

In developing confidence interval for the difference between two population means using two independent samples,we use the pooled estimate $s _ { p }$ 
in estimating the standard error of the sampling distribution of the sample mean difference $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ 
if the populations are normal with equal variances.

Quizplus · Accepted Answer

The pooled estimate $s_p$ is used when the populations are assumed to have equal variances, allowing for a more accurate estimate of the standard error.

In Developing Confidence Interval for the Difference Between Two Population sps _ { p }sp​

In Developing Confidence Interval for the Difference Between Two Population $s _ { p }$