Elementary Statistics (12th Edition)

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

Chapter 7 - Estimates and Sample Sizes - 7-4 Estimating a Population Standard Deviation or Variance - Basic Skills and Concepts: 8

Answer

df=49, $X_{L}^2=32.357$, $ X_{R}^2=71.42$, $\sigma$ is between 0.4862 and 0.7224.

Work Step by Step

$\alpha=1-0.95=0.05.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=50-1=49$. $X_{L}^2= X_{0.975}^2=32.357$ $ X_{R}^2= X_{0.025}^2=71.42$ Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(49)\cdot 0.587^2}{71.42}}=0.4862$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(49)\cdot 0.587^2}{32.357}}=0.7224.$
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