Chapter 9.1, Problem 24E

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:

  $\begin{array}{l}n=2000\\ H_0:p=0.12\\ H_1:\mu >0.12\end{array}$

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

There is enough convincing evidence that the proportion of all U.S. adults who watch the show is greater than 0.12, when the true proportion of all U.S. adults who watch the show is actually 0.12.

A doable consequence is that the show is renewed, while not enough people actually watch the show and therefore the television network could make a loss on the show

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

There is no convincing evidence that the true proportion of all U.S. adults who watch the show is over 0.12, when the true proportion of all U.S. adults who watch the show is actually over 0.12.

A doable consequence is that the show is not renewed, whereas many people would have watched the show and therefore the television network could miss a nice profit on this show.