In constructing a confidence interval estimate for the difference between the means of two independent normally distributed populations,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)never pool the sample variances.

Question

Quizplus · Accepted Answer

We pool the sample variances when the unknown population variances are equal, using the pooled variance formula to increase precision and accuracy in constructing the confidence interval estimate for the difference between the means of two independent normally distributed populations. When the population variances are not equal, we use the separate variances formula, which does not involve pooling. When the population variances are known and equal, we also use the pooled variance formula. Pooling is not necessary when the population means are equal or different, as it only affects the estimation of the variance of the difference between the sample means.

In Constructing a Confidence Interval Estimate for the Difference Between