In constructing a confidence interval estimate for the difference between the means of two normally distributed populations, using two independent samples, which of the following approaches should we follow?
A) Pool the sample variances when the unknown population variances are equal.
B) Pool the sample variances when the population variances are known and equal.
C) Pool the sample variances when the population means are equal.
D) Never pool the sample variances.

Question

Quizplus · Accepted Answer

When the unknown population variances are equal, we should pool the sample variances to increase the degrees of freedom and improve the accuracy of the confidence interval estimate. If the population variances are known and equal, we can also pool the sample variances. However, if the population means are equal, it does not necessarily mean that the population variances are equal, so we should not automatically pool the variances. Additionally, pooling the variances should not be done if there is evidence to suggest that the population variances are unequal or if the sample sizes are very small.

In Constructing a Confidence Interval Estimate for the Difference Between