Chapter 9.3, Problem 83E

(a)

To determine

To Explain: the 95% confidence interval for mean include 10.

Answer to Problem 83E

Yes

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:\mu =10\\ H_{`1}:\mu \ne 10\\ P=0.06\end{array}$

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

  $P=0.06>0.05=5\%\Rightarrow \text{Fail to reject }{H}_0$

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

Since the null hypothesis failed to reject at the 5% significance level the 95% confidence interval contains the value given in the null hypothesis 10.

(b)

To determine

To Explain: the 90% confidence interval for mean include 10.

Answer to Problem 83E

No

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:\mu =10\\ H_{`1}:\mu \ne 10\\ P=0.06\end{array}$

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

  $P=0.06<0.10=10\%\Rightarrow \text{Reject }{H}_0$

A 90% confidence interval associates with a significance test at the 10% significance level.

Since the null hypothesis was reject at the 10% significance level the 95% confidence interval is not having the value given in the null hypothesis 10.