Elementary Statistics (12th Edition)

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

Chapter 8 - Hypothesis Testing - 8-5 Testing a Claim About a Standard Deviation or Variance - Basic Skills and Concepts: 16

Answer

There is sufficient evidence to support that the standard deviation is less than 15.

Work Step by Step

$H_{0}:σ=15$. $H_{a}:σ <15.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(12-1)^2 9.5044^2}{15^2}=4.416.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.05}^2=4.575.$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:4.416<4.575, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the standard deviation is less than 15.
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