Statistical power calculations can be a bit tricky because we need to estimate a value for μ for the alternative hypothesis and we work with both distributions. We are assuming that the mean of the sampling distribution that represents the alternative hypothesis is 5.0. We usually estimate this always from the literature. We begin with the null hypothesis.

The first thing we need to do is calculate the critical value of the mean that cuts off our rejection region for our test (α). Let's set an alpha level of .05. Since this is a test that involves a sample mean, we know that we can use z scores to determine the value of the mean that cuts off that portion of the curve.