Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 7 - Confidence Intervals and Sample - Review Exercises - Section 7-4 - Page 408: 14


$1.54\leq \sigma^2\leq 5.31$

Work Step by Step

Given $n=22, s^2=2.6, c=0.95$ we use the $\chi^2$ table with $df=21, \alpha/2=0.025, 0.975$ to find $\chi^2_{right}=35.479$ and $\chi^2_{left}=10.283$ The confidence interval can be found as $\frac{21\times2.6}{35.479}$ to $\frac{21\times2.6}{10.283}$ The 95% confidence interval of the true variance is $1.54\leq \sigma^2\leq 5.31$
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