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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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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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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