Chapter 9.3, Problem 85E

To determine

To explain: The power of value of 0.764.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Hypothesized population proportion}\left(p_0\right)=0.08\\ \text{Sample size}\left(n\right)=500\\ \text{Level of significance}\left(\alpha \right)=0.05\\ \text{Power = 0}\text{.764}\end{array}$

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=0.08\\ H_a:p>0.08\end{array}$

Concept used:

The power of the test is the probability to do not accept the null hypothesis if the alternative hypothesis is considered to be true

The power of test of $0.764$ implies that there is $76.4\%$ probability to conclude that there are sufficient evidence to favor the alternative hypothesis, that is, $H_0:p>0.08$ .