Chapter 9.1, Problem 32E

To determine

To find: the most appropriate conclusion on the basis of P-value.

Answer to Problem 32E

Because the P-value is large, we fail to reject $H_0$ , we have convincing evidence that at most 50% of city residents support the tax increase.

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:p=0.50\\ H_1:p>0.50\\ P=0.18\end{array}$

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

If the P-value is less than the significance level, then it should be reject the null hypothesis. The common significance levels are $\alpha =0.01$ , $\alpha =0.05$ and $\alpha =\mathrm{0.10.}$ it is observed that the P-value is larger than all common significance levels and therefore it is fails to reject the null hypothesis in each case.

It is fails to reject the null hypothesis, and then there is not enough convincing proof that the alternative hypothesis is true. Therefore there is not convincing proof that the proportion of all residents who help the tax increase is more than 0.50 and therefore there is not convincing proof that a majority of residents helps the tax increase.

Hence, the correct option is (e)