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 - Beyond the Basics: 23

Answer

82.072, 129.635, These values are really close to the actual values.

Work Step by Step

$\alpha=1-0.9=0.1.$ Then we find the critival chi-square values by the given formula:$X_{L}^2=\frac{1}{2}(-z_{\alpha/2}+\sqrt{2k-1})^2=\frac{1}{2}(-1.645+\sqrt{2\cdot105-1})^2=82.072.$ $X_{R}^2=\frac{1}{2}(z_{\alpha/2}+\sqrt{2k-1})^2=\frac{1}{2}(1.645+\sqrt{2\cdot105-1})^2=129.635.$ These values are really close to the actual values.
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