A statistical hypothesis test about the mean of an unknown population tests one of three alternative or research hypotheses

against the null hypothesis

that serves as a benchmark of sorts. The statistic

, when computed from a random sample drawn from the population, follows approximately a

-distribution with

degrees of freedom if the null hypothesis is true. The degree to which the value of this statistic obtained from a given sample falls into the tail(s) of the

-distribution measures our lack of confidence in the truth of the null hypothesis and support for the research hypothesis. The tail area determined by the statistic is called the

-value of the test—the smaller the

-value, the greater the support for the research hypothesis. For the sake of a clear decision, sometimes a boundary

-value,

, is specified. If the

-value of the test is smaller than

, then the null hypothesis is rejected.