In testing the difference between two population means using two independent samples,we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference $\overline { \mathrm { x } } _ { 1 } - \overline { \mathrm { x } } _ { 2 }$ if the:
A) sample sizes are both large.
B) populations are at least normally distributed with equal variances.
C) populations are non-normal with unequal variances.
D) All of these are required conditions.

Question

Quizplus · Accepted Answer

The pooled variance is used when we have two independent samples from normally distributed populations with equal variances. In this case, the pooled variance is a weighted average of the sample variances from each of the two samples. If the population variances are not equal or the populations are non-normal, then the assumption of normality may not hold and we may need to use non-parametric tests or other procedures. If the sample sizes are both large, we can use the central limit theorem to justify the use of the pooled variance. However, this is not a sufficient condition on its own for using the pooled variance.

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In Testing the Difference Between Two Population Means Using Two $\overline { \mathrm { x } } _ { 1 } - \overline { \mathrm { x } } _ { 2 }$