Chapter 9.1, Problem 31E

To determine

To find: the correct interpretation of the P-value.

Answer to Problem 31E

Assuming that 50% of residents support the tax increase, there is an 18% probability that the sample proportion would be 0.527 or greater by chance alone.

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:p=0.50\\ H_1:p>0.50\\ P=0.18\\ \widehat{p}=158/300=0.527\end{array}$

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

The P-value is the probability that the proportion is more extreme than the sample proportion $\widehat{p}$ type I error, when the null hypothesis $H_0$ is true.

The null hypothesis is true, if the proportion of all city residents who help the tax increase is equal to 0.50 and therefore when 50% of the residents help the tax increase.

Since the statement of the probability also requires including the sample proportion

Hence, the correct option is (c)