Answered: Cynthia, Mary, Mika, and Sallieof Hu’s…

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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Cynthia, Mary, Mika, and Sallieof Hu’s Ur Dedi Cerveza Corp. conducted a survey on their 12-ounce cans to be sure that the variance of the amount of beer, in each can, was no more than 0.02square ounces. They collected a random sample of twenty cans of their 12-ounce beer, pulled from their production line, and got a sample variance of 0.015square ounces. Assume that the amount of beer in all 12-ounce cans to be normally distributed. Help them: a.Construct a 95% confidence interval for the population variance.

b.Construct a 99% confidence interval for the standard deviation.

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

Introduction

Confidence interval for population variance is calculated using the sample variance and chi square critical value with degree of freedom. The confidence interval is defined as follows :

$\begin{array}{rcl} \frac{(n - 1) s^{2}}{χ_{\frac{α}{2}}^{2}} & \leq & σ^{2} \leq \frac{(n - 1) s^{2}}{χ_{1 - \frac{α}{2}}^{2}} \end{array}$

where $σ^{2}$ is population variance and $s^{2}$ is the sample variance.

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