Chapter EP, Problem 12.6.3EP

To determine

To find: The $95\%$ confidence interval.

Answer to Problem 12.6.3EP

The $95\%$ confidence interval estimate is $49.0714\le \mu \le 50.9286$ .

Explanation of Solution

Given information:

The given values is $\overline{x}=50$ , $s=6.7$ and $n=200$ .

Calculation:

The mean $\overline{x}=50$ , the standard deviation $s=6.7$ and the size of the sample is $n=200$ .

The $95\%$ confidence interval formula is,

  $CI=\overline{x}\pm 1.96\frac{s}{\sqrt{n}}$ .... (1)

Substitute the values in equation (1)

  $\begin{array}{c}CI=\overline{x}\pm 1.96\frac{s}{\sqrt{n}}\\ =50\pm 1.96\frac{6.7}{\sqrt{200}}\\ =50\pm 1.96\times 0.4738\\ \approx 50\pm 0.9286\end{array}$

The lower bound of the interval is,

  $\begin{array}{c}l=50-00.9286\\ =49.0714\end{array}$

The upper bound of the interval is,

  $\begin{array}{c}u=50+0.9286\\ =50.9286\end{array}$

Therefore, the $95\%$ confidence interval estimate is $49.0714\le \mu \le 50.9286$ .