Chapter 11.6, Problem 14PPS

To determine

To identify: The null, the alternative hypotheses, and the claim of the given statement.

Answer to Problem 14PPS

The alternative hypothesis of the statement is $H_a:\mu <18$ , the null hypothesis is $H_0:\mu \ge 18$ , and the claim is $H_0:\mu \ge 18$ .

Explanation of Solution

Given Information:

The given statement is, “A singer plays at least $18$ songs at every concert”.

Concept used:

The null hypothesis is a statement of the equality to be tested and the alternative hypothesis is a statement of inequality that is the component of the null hypothesis. The claim can be the part of the null or the alternative hypothesis.

As per the given statement, the alternative hypothesis is,

  $H_a:\mu <18$

The null hypothesis is,

  $H_0:\mu \ge 18$

The claim is $H_0:\mu \ge 18$ .

Thus, the alternative hypothesis of the statement is $H_a:\mu <18$ , the null hypothesis is $H_0:\mu \ge 18$ , and the claim is $H_0:\mu \ge 18$ .