Use the given statement to represent a claim. Write its complement and state which is and

Which is .

P < 0.75

*Solution*

Begin by finding the complement of the claim. The complement of a claim is the statement that must be true when the claim is false.

The complement of p < 0.75 is p ≥ 0.75.

The null hypothesis is a statistical hypothesis that contain a statement of equality, such as ≤ , = . or ≥.

The alternative hypothesis is the complement of the null hypothesis. It is a statement that must be true if is false, and it contain a statement of strict inequality, such as >, ≠, or <.

The null hypothesis is :p≥0.75 because the null hypothesis must contain statement of equality.

The alternative hypothesis is : p<0.75 because alternative hypothesis must contain a statement of strict inequality.

Therefore, the null and alternative hypotheses are below.

:p ≥ 0.75

:p < 0.75