Chapter 14.5, Problem 25E

To determine

Find the interval about the sample mean having $5\%$ confidence level.

Answer to Problem 25E

  $\left[5.23,5.53\right]$

Explanation of Solution

Given information:

Given: $\sigma =0.67,N=80,\overline{X}=5.38$

Calculation:

Here, $5\%$ confidence level means when $P=95\%$ .

Now,

  $\begin{array}{l}P=95\%correspondstot=1.96\\ {\sigma }_{\overline{X}}=\frac{\sigma }{\sqrt{N}}\\ {\sigma }_{\overline{X}}=\frac{0.67}{\sqrt{80}}=0.075\\ Interval:\\ \left[\overline{X}-t{\sigma }_X,\overline{X}+t{\sigma }_X\right]\\ \left[5.23,5.53\right]\end{array}$

Hence, the required answer is $\left[5.23,5.53\right]$ .