Essentials of Statistics (5th Edition)

Published by Pearson
ISBN 10: 0-32192-459-2
ISBN 13: 978-0-32192-459-9

Chapter 8 - Hypothesis Testing - 8-5 Testing a Claim About a Standard Deviation or Variance - Page 423: 6

Answer

There is sufficient evidence to support that the volumes have a standard deviation less than 0.15.

Work Step by Step

$H_{0}:\sigma=0.15$. $H_{a}:\sigma < 0.15.$ Hence the value of the test statistic: $X^2=\frac{(n-1)s^2}{\sigma^2}=\frac{(36-1)^20.09^2}{0.15^2}=12.6.$ The critical value is the $x^2$ value corresponding to the found significance level, hence:$X_{1-0.05}^2=\frac{26.509+18.493}{2}=22.501.$If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:12.6<22.501, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the volumes have a standard deviation less than 0.15.
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