Chapter 9.3, Problem 86E

a.

To determine

To check: Whether the confidence interval for the population mean would include 15 or not.

Answer to Problem 86E

Yes, it would contain the value 15.

Explanation of Solution

Given:

P -value is 0.03

Confidence level = 99%

Concept used:

Reject the null hypothesis, if P -value is less than the significance level.

Calculation:

The level of significance is:

  $\begin{array}{c}\text{Level of significance}\left(\alpha \right)=1-\text{Confidence level}\\ \text{=1-0}\text{.99}\\ \text{=0}\text{.01}\end{array}$

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =15\\ H_a:\mu \ne 15\end{array}$

Here P -value (0.03) >$\alpha \left(0.01\right)$ . The null hypothesis is not rejected. Thus, it could be said that the confidence level would contain 15.

b.

To determine

To check: Whether the confidence interval for the population mean would include 15 or not.

Answer to Problem 86E

No, it would not contain the value 15.

Explanation of Solution

Given:

Confidence level = 95%

Concept used:

Reject the null hypothesis, if P -value is less than the significance level.

Calculation:

The level of significance is:

  $\begin{array}{c}\text{Level of significance}\left(\alpha \right)=1-\text{Confidence level}\\ \text{=1-0}\text{.95}\\ \text{=0}\text{.05}\end{array}$

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =15\\ H_a:\mu \ne 15\end{array}$

Here P -value (0.03) < $\alpha \left(0.05\right)$ . The null hypothesis is rejected. Thus, it could not be said that the confidence level would contain 15.