If the populations are normally distributed and 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 populations are normally distributed but have unequal variances, the "unpooled" formula for the t-statistic is appropriate because it does not assume equal variances, unlike the "pooled" formula.

If the Populations Are Normally Distributed and the Variances of the Two