Chapter 9, Problem 1RE

Find the critical t-value for constructing a confidence interval for a population mean at the given level of confidence for the given sample size, n.

1. a. 99% confidence; n = 18
2. b. 90% confidence; n = 27

To determine

The critical value that corresponds to the sample of size $n=18$ and 99% confidence level.

Answer to Problem 1RE

The critical value is 2.898.

Explanation of Solution

Calculation:

Critical value:

For 99% confidence level

$\begin{array}{c}1-\alpha =1-0.99\\ \alpha =0.01\\ \frac{\alpha }{2}=\frac{0.01}{2}\\ =0.005\end{array}$

The degrees of freedom is,

$\begin{array}{c}d.f=n-1\\ =18-1\\ =17\end{array}$

From Table VII of the t distribution in Appendix A, the critical value that corresponds to the 17 degrees of freedom and 0.005 area in right tail is 2.898.

Thus, the critical value is 2.898.

To determine

The critical value that corresponds to the sample of size $n=27$ and 90% confidence level.

Answer to Problem 1RE

The critical value is 1.706

Explanation of Solution

Calculation:

Critical value:

For 90% confidence level

$\begin{array}{c}1-\alpha =1-0.90\\ \alpha =0.1\\ \frac{\alpha }{2}=\frac{0.1}{2}\\ =0.05\end{array}$

The degrees of freedom is,

$\begin{array}{c}d.f=n-1\\ =27-1\\ =26\end{array}$

From Table VII of the t distribution in Appendix A, the critical value that corresponds to the 26 degrees of freedom and 0.05 area in right tail is 1.706.

Thus, the critical value is 1.706.