I guess that you already know a little bit about hypothesis testing. For instance, you might have carried out tests in which you tried to reject the hypothesis that your sample comes from a population with a hypthesized mean µ. As you know that the sample mean follows a t-distribution (or the normal distribution in case of huge samples), you can define a rejection region based on a specific significance level α. In a one-sided test, sample means which are less than a critical value CV might be considered to be rather unlikely. If the obtained sample’s mean falls into this region, the hypothesis gets rejected at this particular signficance level α.
![Distribution of sample mean and rejection region for one-sided test](http://www.insight-things.com/wp-content/uploads/2016/04/rejection_region-1024x589.png)
Distribution of sample mean and rejection region for one-sided test
We know the chance of rejecting the hypothesis although it’s true (Type I error), because it is the chance of obtaining just one of those values from the rejection region (plotted red). But how likely are we to reject a hypothesis if it’s indeed false? In other words: How small is the type II error? more →