Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 7 - Estimates and Sample Sizes - Review - Review Exercises: 10

Answer

σ is between 3.61 and 12.33

Work Step by Step

$\alpha=1-0.95=0.05.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=7-1=6$. $X_{L}^2= X_{0.975}^2=1.237$ $ X_{R}^2= X_{0.025}^2=14.449$ Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(6)\cdot 5.6^2}{14.449}}=3.61$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(6)\cdot 5.6^2}{1.237}}=12.33.$
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