When we are comparing the population means from two normally distributed populations based on independent random samples,the pooled estimate of the variance $s _ { p } ^ { 2 }$
is used if both population standard deviations are known.

Question

When we are comparing the population means from two normally distributed populations based on independent random samples,the pooled estimate of the variance $s _ { p } ^ { 2 }$ 
is used if both population standard deviations are known.

Quizplus · Accepted Answer

The pooled estimate of the variance $s _ { p } ^ { 2 }$ is used when the population standard deviations are unknown but assumed to be equal. When both population standard deviations are known, there is no need to estimate variance using sample data.

When We Are Comparing the Population Means from Two Normally sp2s _ { p } ^ { 2 }sp2​

When We Are Comparing the Population Means from Two Normally $s _ { p } ^ { 2 }$