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 if the populations are normal with equal variances.

When testing the difference between two population means using two independent samples and assuming normality and equal variances, we use the pooled variance to estimate the standard error of the sampling distribution of the sample mean difference. This is because the pooled variance is a weighted average of the sample variances from each group, which accounts for the variation within each group and provides a more accurate estimate of the population variance.