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: 10

Answer

σ is between 2.133 and 3.093.

Work Step by Step

$\alpha=1-0.9=0.1.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=40-1=39$. $X_{L}^2= X_{0.975}^2=26.509$ $ X_{R}^2= X_{0.025}^2=55.758$ Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(39)\cdot 2.55^2}{55.758}}=2.133$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(39)\cdot 2.55^2}{26.509}}=3.093.$
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