In testing the difference between the means of two normally distributed populations with known population standard deviations,we can only use a two-sided test.

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We can use either a two-sided test or a one-sided test depending on the hypothesis we are testing. A two-sided test is used when we are interested in determining if there is any difference between the means, while a one-sided test is used when we are interested in determining if one mean is greater than or less than the other mean.

In Testing the Difference Between the Means of Two Normally