When performing a hypothesis test for the difference in 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 the individual standard deviations, not the pooled standard deviation. The pooled standard deviation is used when the standard deviations are unknown and assumed to be equal.

When Performing a Hypothesis Test for the Difference in the Means