Answered: Find the 90 percent confidence interval…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Find the 90 percent confidence interval for the variance and standard deviation for the time it takes state police inspector to check a truck for safety if a sample of 27 trucks has a standard deviation of 8.9 minutes. Assume the variable is normally distributed

Expert Solution

Step 1

Solution :

Given : n = 27

s = 8.9 minutes

$α$ = 0.1

Confidence interval for population variance :

CI = ( $\frac{(n - 1) s^{2}}{≁_{\frac{α}{2}}^{2}} \leq σ^{2} \leq \frac{(n - 1) s^{2}}{≁_{1 - \frac{α}{2}}^{2}}$ )

= $\frac{(27 - 1) 8 . 9^{2}}{≁_{\frac{0.1}{2}}^{2}} \leq σ^{2} \leq \frac{(27 - 1) 8 . 9^{2}}{≁_{1 - \frac{0.1}{2}}^{2}}$ )

= ( $\frac{2059.46}{38.88} \leq σ^{2} \leq \frac{2059.46}{15.37}$

= ( 52.96 $\leq$ $σ^{2}$ $\leq$ 133.99)

Answer : 90% confidence interval for population variance is (52.96 minutes, 133.99 minutes)

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