Chapter 9.3, Problem 85E

a.

To determine

To explain: Whether the 95% confidence interval includes 10 or not.

Answer to Problem 85E

Yes, it does include 10.

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:\mu =10\\ P-value=0.06\end{array}$

Concept used:

Reject, $H_0$ , if level of significance $\left(\alpha \right)<P-value$ .

Calculation:

The null and alternative hypotheses could be written as:

  $\begin{array}{l}{H}_0:\mu =10\\ H_a:\mu \ne 10\end{array}$

The level of significance is 0.05.

Here, $p-value\left(0.06\right)>\alpha \left(0.05\right)$

Thus, the null hypothesis is not rejected. So, it could be concluded that 95% confidence interval for $\mu$ will includes 10

b.

To determine

To explain: Whether the 90% confidence interval includes 10 or not.

Answer to Problem 85E

No, it does not include 10.

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:\mu =10\\ P-value=0.06\end{array}$

Concept used:

Reject, $H_0$ , if level of significance $\left(\alpha \right)<P-value$ .

Calculation:

The null and alternative hypotheses could be written as:

  $\begin{array}{l}{H}_0:\mu =10\\ H_a:\mu \ne 10\end{array}$

The level of significance is 0.10.

Here, $p-value\left(0.06\right)<\alpha \left(0.10\right)$

Thus, the null hypothesis is rejected. So, it could not be concluded that 90% confidence interval for $\mu$ will include 10.