We show how to test hypotheses for coefficient alpha in three different situations: (1) Hypothesis tests of whether coefficient alpha equals a prespecified value. (2) Hypothesis tests involving two statistically independent sample alphas as may arise when testing the equality of coefficient alpha across groups. (3) Hypothesis tests involving two statistically dependent sample alphas as may arise when testing the equality of alpha across time, or when testing the equality of alpha for two test scores within the same sample. We illustrate how these hypotheses may be tested in a structural equation modeling framework under the assumption of normally distributed responses and also under asymptotically distribution free (ADF) assumptions. The formulas for the hypothesis tests and computer code are given for four different applied examples.