Chapter 9.1, Problem 23E

To determine

To Explain: the Type-I error and Type-II error in this setting, and give a possible consequence of each.

Explanation of Solution

Given:

  $\begin{array}{l}n=50\\ H_0:\mu =\$85,000\\ H_1:\mu >\$85,000\end{array}$

Type I error is rejecting the null hypothesis $H_0$ , once the null hypothesis $H_0$ is true.

There is enough convincing proof that the mean financial gain of these living close to the restaurant is bigger than 85,000 once the mean financial gain of these living close to the restaurant is really 85,000.

A doable consequence is that open a restaurant in this area, whereas the financial gain of the folks living in this area is not large enough and therefore restaurant could depart of business.

Type II error: Fail to reject the null hypothesis $H_0$ , once the null hypothesis $H_0$ is false

There is no sufficient convincing proof that the mean financial gain of these living close to the restaurant is bigger than 85,000, when the mean financial gain of these living close to the restaurant is really over 85,000.

A doable consequence is that not open a restaurant in this area, whereas the financial gain of the folks living during this space is giant enough and therefore it might miss out on a profitable location.