In general,a directional test will always be more powerful than a corresponding nondirectional test if the actual population mean and the hypothesized population mean differ in the specified direction.

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This is true because with a directional test, all the rejection region is in one tail of the distribution, which makes it more focused and concentrated. Therefore, if the true population mean is in the specified direction, it is more likely to fall in the rejection region, leading to a higher chance of rejecting the null hypothesis. In contrast, a nondirectional test has a rejection region on both tails of the distribution, which spreads out the critical values and reduces the power of the test. Therefore, a directional test is preferred when we have a specific expectation about the direction of the effect.

In General,a Directional Test Will Always Be More Powerful Than