A Type I Error occurs when rejecting the null hypothesis in the universe in which it is in fact true. $\alpha$ is the probability of a Type 1 error, the the probability of rejecting the null hypothesis when it is in fact true. $\alpha$ is called the [[level of significance]] or sometimes the **size** of the test. $\alpha = P \Big( Z < \frac{c - \mu_0}{\sqrt{\sigma^2/n}} \Big )$ $z_{\alpha} = \frac{c - \mu_0}{\sqrt{\sigma^2/n}}$ $c = \mu_0 + z_{\alpha}\sqrt{\frac{\sigma^2}{n}}$ Here, $c$ is the upper bound of a [[confidence interval]] around $\mu_0$, the null hypothesis.