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: 11

Answer

σ is between 30.9 and 67.5.

Work Step by Step

$\alpha=1-0.99=0.01.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=24-1=23$. $X_{L}^2= X_{0.975}^2=9.26$ $ X_{R}^2= X_{0.025}^2=44.181$ Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(23)\cdot 42.8^2}{44.181}}=30.9$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(23)\cdot 42.8^2}{9.26}}=67.5.$
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