If the populations are normally distributed and the variances of the two populations are equal, it is appropriate to use the "pooled" formula to determine the t-statistic for the hypothesis test of the difference in the two population means.

Question

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When the populations are normally distributed and have equal variances, the "pooled" formula for the t-statistic is appropriate because it assumes homogeneity of variances, allowing for a more precise estimate of the standard error of the difference between the two means.

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