If the variances of the two populations are not equal, it is appropriate to use the "unpooled" formula to determine the t statistic for the hypothesis test of the difference in the two population means.

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When the variances of the two populations are not equal, it is appropriate to use the "unpooled" formula for calculating the standard error of the difference between the means. This involves using separate estimates of the population variances for each group, rather than assuming they are equal and pooling them together. This results in a modified t statistic that takes into account the differences in variances between the two groups.

If the Variances of the Two Populations Are Not Equal