Null hypothesis

The null hypothesis, written $H_0$ (read H-naught), is the skeptical starting point that nothing unusual is going on. It always contains an equals sign, fixing the parameter at one value so the test can build a sampling distribution around it. For example, testing a new teaching method against the old one uses $H_0: \mu_{\text{new}} = \mu_{\text{old}}$, the claim of no improvement. A test never proves $H_0$; it either rejects it or fails to reject it for lack of evidence.