Chapter 9.1, Problem 8E

a)

To determine

To find: The mistake in the provided hypothesis and provide the correct hypothesis.

Answer to Problem 8E

The appropriate hypotheses are:

  $\begin{array}{l}{H}_0:p=0.37\\ H_a:p>0.37\end{array}$

Explanation of Solution

Given:

The provided hypotheses are:

  $\begin{array}{l}{H}_0:\widehat{p}=0.37\\ H_a:\widehat{p}>0.37\end{array}$

Calculation:

Hypothesis is conducted for the population parameter not the sample statistics. Here, it is required to change the provided hypothesis by the population proportion. The correct null and alternative hypotheses could be written as:

  $\begin{array}{l}{H}_0:p=0.37\\ H_a:p>0.37\end{array}$

b)

To determine

To find: The mistake in the provided hypothesis and provide the correct hypothesis.

Answer to Problem 8E

The appropriate hypotheses are:

  $\begin{array}{l}{H}_0:\mu =3000\\ H_a:\mu <3000\end{array}$

Explanation of Solution

Given:

The provided hypotheses are:

  $\begin{array}{l}{H}_0:\mu =3000\\ H_a:\mu \le 2999\end{array}$

Calculation:

Inequalities are shown in the null hypothesis not the alternative hypothesis. Here, inequality has been provided in the alternative hypothesis and value of the parameter must be same in both the parameters. So, it is required to replace 2999 by 3000 and $\le \text{ by }<$ .

The hypotheses are:

  $\begin{array}{l}{H}_0:\mu =3000\\ H_a:\mu <3000\end{array}$