Chapter 9.1, Problem 9E

(a)

To determine

To Explain: the mean for the null hypothesis to be true in this setting.

Answer to Problem 9E

  $H_0:p=75\%=0.75$

Explanation of Solution

Given:

Claim is proportion is less than 75%

The null hypothesis statement is that the population value is equal to the value given in the claim:

  $H_0:p=75\%=0.75$

If the null hypothesis $H_0:p=75\%=0.75$ is true, then this means that 75% of all students in researcher’s school completed their homework assignments last night.

(b)

To determine

To Explain: the P-value.

Explanation of Solution

Given:

  $\begin{array}{l}P-\text{value =0}\text{.1265 =12}\text{.65\%}\\ \widehat{p}=68\%=0.68\end{array}$

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 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.

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

The P-value is the probability of getting the value of the test statistic, or a value more extreme, when the null hypothesis is true.

There is a 12.65% possibility that the sample proportion of students in the sample who finished their homework assignments last night is 0.68 or less, when the population proportion of all students at the school who finished their homework assignment last night is 0.75.