The power of a hypothesis test is the probability that the sample mean will be in the critical region if the treatment has an effect.

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This statement accurately defines the power of a hypothesis test, which is the ability of the test to detect a true difference or effect if one exists. A high power means that the test is more likely to correctly reject the null hypothesis and conclude that there is a significant difference or effect, whereas a low power means that the test is more likely to incorrectly fail to reject the null hypothesis and miss a true difference or effect. The critical region is the part of the distribution of the test statistic that corresponds to rejection of the null hypothesis at a specified level of significance or alpha, so if the sample mean falls within this region, it suggests that the treatment has had an effect and the null hypothesis should be rejected.

The Power of a Hypothesis Test Is the Probability That