Chapter 9.1, Problem 30E

To determine

To find: the correct option for the type-I error in the context of the study occurs if the city council.

Answer to Problem 30E

Finds convincing evidence that a majority of residents supports the tax increase, when in reality there isn’t convincing evidence that a majority supports the increase.

Explanation of Solution

Given:

  $p$ is the proportion of all city residents who help 1% increase in the sales tax to fund repairs.

  $\begin{array}{l}{H}_0:p=0.50\\ H_1:p>0.50\end{array}$

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

If there’s rejecting the null hypothesis, then there is enough convincing proof that the alternative hypothesis is true. So there’s enough convincing proof that the proportion of all residents who help the tax increase is over 0.50 and therefore there’s convincing proof that a majority of residents helps the tax increase.

The null hypothesis is true, if the proportion of all city residents who help the tax increase is equal to 0.50 and therefore once there’s not convincing proof that the bulk helps the increase.

Hence, the correct option is (a)