Problem 397

Use the given statement to represent a claim. Write its complement and state which is H_{0} and

Which is H_{a}.

P < 0.75




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 H_{0} is a  statistical hypothesis that contain a statement of equality, such as ≤ , = . or ≥.

The alternative hypothesis H_{a} is the complement of the null hypothesis. It is a statement that must be true if H{0} is false, and it contain  a statement of strict inequality, such as >, ≠, or <.

The null hypothesis is H_{0}:p≥0.75 because the null hypothesis must contain statement of equality.

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

Therefore, the null and alternative hypotheses are below.

H_{0} :p ≥ 0.75

H_{a}:p < 0.75


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