Page "Null hypothesis" Paragraph 26

A point hypothesis is more complicated to describe.

The term arises in contexts where the set of all possible population distributions is put in parametric form.

A point hypothesis is one where exact values are specified for either all the parameters or for a subset of the parameters.

Formally, the case where only a subset of parameters is defined is still a composite hypothesis ; nonetheless, the term point hypothesis is often applied in such cases, particularly where the hypothesis test can be structured in such a way that the distribution of the test statistic ( the distribution under the null hypothesis ) does not depend on the parameters whose values have not been specified under the point null hypothesis.

Careful treatments of point hypotheses for subsets of parameters do consider them as composite hypotheses and study how the p-value for a fixed critical value of the test statistic varies with the parameters that are not specified by the null hypothesis.