In estimating the difference between two population means based on small, independent samples from the two populations, two important assumptions are that the populations each be normally distributed and the populations have equal variances.

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For small, independent samples, the assumption of normality ensures the sampling distribution of the difference between means approximates a normal distribution, and the assumption of equal variances (homoscedasticity) is crucial for the validity of the test statistics used in such comparisons.

In Estimating the Difference Between Two Population Means Based on Small