Chapter 11, Problem 15PT

To determine

To identify: The null and alternative hypotheses for each statement and then identify the statement that represents the claim.

Answer to Problem 15PT

The null and alternative hypotheses are $H_0\to \mu =5$ and $H_a\to \mu \ne 5$ .

Explanation of Solution

Given:

The statement is “A restaurant owner says that each milk shake contains 5 strawberries.”

Calculation:

A restaurant owner says that each milk shake contains 5 strawberries that means $\mu =5$ .

A restaurant owner says that each milk shake does not contain 5 strawberries that means $\mu \ne 5$ .

The null hypothesis is a statement of equality while the alternative hypothesis is an inequality or the complement of the null hypothesis.

The statement that represents the claim is as follows.

  $\begin{array}{l}{H}_0\to \mu =5\\ H_a\to \mu \ne 5\end{array}$

Therefore, the null and alternative hypotheses are $H_0\to \mu =5$ and $H_a\to \mu \ne 5$ .