Chapter 9.3, Problem 84E

(a)

To determine

To Explain: the 99% confidence interval for mean include 15.

Answer to Problem 84E

Yes

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:\mu =15\\ H_1:\mu \ne 15\\ P=0.03\end{array}$

A 99% confidence interval corresponds with a significance test at the 100%-99%=1% significance level.

If the P-value is smaller than the significance level then the null hypothesis is rejected.

  $P=0.03>0.01=1\%\Rightarrow \text{Fail to reject }{H}_0$

Since the null hypothesis failed to reject at the 1% significance level, the 99% confidence interval is having the value given in the null hypothesis

(b)

To determine

To Explain: the 95% confidence interval for mean include 15.

Answer to Problem 84E

No

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:\mu =15\\ H_1:\mu \ne 15\\ P=0.03\end{array}$

A 95% confidence interval associates with a significance test at the 100%-95%=5% significance level.

If the P-value is lesser than the significance level then the null hypothesis is rejected.

  $P=0.03<0.05=5\%\Rightarrow \text{Reject }{H}_0$

Since the null hypothesis reject at the 5% significance level, the 95% confidence interval is not having the value given in the null hypothesis