Chapter 11, Problem 16PT

To determine

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

Answer to Problem 16PT

The null and alternative hypotheses are $H_0\to \mu \le 56$ and $H_a\to \mu >56$ .

Explanation of Solution

Given:

The statement is “A valet says that no more than $56$ cars can be parked in the parking lot at one time.”

Calculation:

A valet says that no more than $56$ cars can be parked in the parking lot at one time that means $\mu \le 56$ .

A valet says that more than $56$ cars can be parked in the parking lot at one time that means $\mu >56$ .

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.

  $\begin{array}{l}{H}_0\to \mu \le 56\\ H_a\to \mu >56\end{array}$

Therefore, the null and alternative hypotheses are $H_0\to \mu \le 56$ and $H_a\to \mu >56$ .