Chapter 9.3, Problem 81E

To determine

To find: The confidence interval.

Answer to Problem 81E

The confidence interval is $\left(11.561,11.472\right)$

Explanation of Solution

Given:

Data:

11.627
11.613
11.493
11.602
11.36
11.374
11.592
11.458
11.552
11.463
11.383
11.715
11.485
11.509
11.429
11.477
11.57
11.623
11.472
11.531

Formula:

The confidence interval for population mean is:

  $\overline{x}-t_{\alpha /2}\times \frac{s}{\sqrt{n}}<\mu <\overline{x}+t_{\alpha /2}\times \frac{s}{\sqrt{n}}$

Calculation:

The sample mean and standard deviation are 11.5164 and 0.0950.

Degree of freedom = n -1 = 20-1 = 19

From critical value table, the t-value is 2.093.

The confidence interval is computed as:

  $\begin{array}{l}\overline{x}-t_{\alpha /2}\times \frac{s}{\sqrt{n}}<\mu <\overline{x}+t_{\alpha /2}\times \frac{s}{\sqrt{n}}\\ 11.5164-2.096\times \frac{0.0950}{\sqrt{20}}<\mu <11.5164+2.096\times \frac{0.0950}{\sqrt{20}}\\ \left(11.561,11.472\right)\end{array}$

The confidence interval is $\left(11.561,11.472\right)$ .