The table below shows the combination of the decisions we can make when we test our hypothesis (reject or fail to reject) and the true but unknown population represented in the null hypothesis (true or false). If our research hypothesis is correct, then the null hypothesis will be false, and we will want to reject this false null. However, if our research hypothesis is incorrect, the null will be true, and we will want to fail to reject a true null.

We can also place our four outcomes on the sampling distributions we use in our hypothesis tests.