We use a z score and the z table to determine the areas under the curve. We want to know the area above this point. Here is the formula (remember that this is a sampling distribution, so we use the standard error of the mean, and not σ, in our formula).

To continue our example, μ = 5.0, σ = 2.0, n = 30, and the sample mean is 5.40. The population mean that we use in this formula is our best guess based on the literature.

A z score of 1.09 cuts off the upper portion of the distribution. From the z table, we learn that this has a value of .1379. This is the probability that we would fail to reject the null hypothesis if we randomly sampled 30 students from the alternative population.

To determine our statistical power, we just calculate 1 - β. 1 - .1379 = .8621. This is the probability that we would reject the null hypothesis if we randomly sampled 30 students from the alternate population.