A hypothesis test is an inferential method that uses sample data to examine a claim about the mean $\mu$ of a population. Because the population mean is almost always unknown, it is common to be suspicious about the truthfulness of any assumption about its value. The following are typical claims about the mean of a population.

Typical Claims About the Mean
The mean is equal to a specific value, $\mu =k.$	The mean is greater than a specific value, $\mu >k.$	The mean is less than a specific value, $\mu <k.$

Before making a hypothesis test, two hypotheses need to be specified, the null hypothesis and the alternative hypothesis. These hypotheses must be mutually exclusive. The null hypothesis $H_0$ is assumed to be true. The hypothesis test puts the null hypothesis on trial to see if there is strong evidence against it. If so, the alternative hypothesis $H_a$ is accepted instead.

• $H_0:$ The hypothesis that is examined.
• $H_a:$ The hypothesis that is accepted if there is strong evidence to reject $H_0.$

Once the two hypotheses are set, sample data needs to be collected and analyzed to determine whether the sample mean falls within the critical region to either accept or reject the null hypothesis. The tests of significance determine the position of the critical region whose area equals the significance level $\alpha .$