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 424: 11

Answer

There is not sufficient evidence to reject that the cigarettes have a standard deviation not equal to 3.2.

Work Step by Step

$H_{0}:σ=3.2$. $H_{a}:σ\ne3.2.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(25-1)^2 3.7^2}{3.2^2}=32.086.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.975}^2=12.401, X_{0.025}^2=39.364.$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:12.401<32.086<39.364, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to reject that the cigarettes have a standard deviation not equal to 3.2.
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