In constructing a confidence interval estimate for the difference between the means of two normally distributed populations, using two independent samples, we:
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) pool the sample variances when the unknown population variances are unequal
E) never pool the sample variances

Question

Quizplus · Accepted Answer

When the unknown population variances are equal, we can pool the sample variances to increase the sample size and improve the accuracy of our estimate. This results in a smaller standard error and a narrower confidence interval. However, if we have reason to believe that the population variances are unequal, we should not pool the sample variances and instead use a modified formula for the standard error.

In Constructing a Confidence Interval Estimate for the Difference Between