If two population variances are known,the test for differences in the two population means does not require the populations to be normally distributed if the sample sizes are large.

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Quizplus · Accepted Answer

This is the assumption of the independent samples t-test when the sample sizes are large (n≥30) and the variances are known. However, if the sample sizes are small, then the populations need to be normally distributed, and if the variances are unknown and assumed to be equal, then the populations can have different shapes but have to be also normally distributed.

If Two Population Variances Are Known,the Test for Differences in the Two