When performing a hypothesis test for the difference between the means of two independent populations where the standard deviations are known, it is necessary to use the pooled standard deviation in calculating the test statistic.

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When the standard deviations of two independent populations are known, the test statistic is calculated using those known standard deviations directly, rather than pooling them. Pooling is used when the population standard deviations are unknown and assumed to be equal, and sample standard deviations are used as estimates.

When Performing a Hypothesis Test for the Difference Between the Means