Chapter 9.1, Problem 15E

To determine

To find: the conclusion would make at the $\alpha =0.05$ level.

Explanation of Solution

Given:

  $\begin{array}{l}P=0.1265=12.65\%\\ \alpha =0.05\end{array}$

Given claim is proportion is less than 75%.

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

  $\begin{array}{l}{H}_0:p=75\%=0.75\\ H_a:p<0.75\end{array}$

If the P-value is smaller than the significance level $a$ , then reject the null hypothesis:

  $0.1265>0.05\Rightarrow \text{Fail to reject }{H}_0$

There is not enough convincing evidence to help the claim that less than 75% of the students at researcher’s school finished their homework last night.