Chapter 9.1, Problem 10E

(a)

To determine

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

Answer to Problem 10E

The correct mean score for the students who are at least 30 years of age is 115.

Explanation of Solution

Given:

From the previous exercise

  $\begin{array}{l}{H}_0:\mu =115\\ H_a:\mu >115\end{array}$

  $\mu$ is the population mean score of students who are at least 30 years of age.

If the null hypothesis $H_0:\mu =115$ is true, then this means that the true mean score for students who are at least 30 years of age is 115

(b)

To determine

To Explain: the P-value.

Answer to Problem 10E

The P-value is if the population mean is equal to 115, then there is possibility of 1.01% of getting a random sample with a sample mean of 125.7 or more.

Explanation of Solution

Given:

  $\begin{array}{l}n=45\\ \overline{x}=125.7\\ s=29.8\\ P=0.0101=1.01\%\end{array}$

Result previous exercise:

  $\begin{array}{l}{H}_0:\mu =115\\ H_a:\mu >115\end{array}$

The P-value is if the population mean is equal to 115, then there is possibility of 1.01% of getting a random sample with a sample mean of 125.7 or more.