In estimating a confidence interval for the difference between two means, when the samples are independent and the standard deviations are unknown, it can be acceptable for there to be small violations of the assumptions of normality and equal variances, especially when the sample sizes are equal.

Question

Quizplus · Accepted Answer

When the sample sizes are equal, the Central Limit Theorem suggests that the sampling distribution of the difference between two means will be approximately normal, even if the original populations are not perfectly normal. Additionally, equal sample sizes can mitigate the effects of unequal variances between the two groups.

In Estimating a Confidence Interval for the Difference Between Two