## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 9 - Inferences from Two Samples - 9-5 Two Variances or Standard Deviations - Basic Skills and Concepts: 14

#### Answer

Reject the null hypothesis.

#### Work Step by Step

$H_{0}:\sigma_1=sigma_2,$ $H_{a}:\sigma_1\ne \sigma_2$. :$F=\frac{s_1^2}{s_2^2}=\frac{18.6028^2}{8.9604^2}=4.31.$ The critical values by the table with df=min(23,13)=13: $f_{0.025}$ is between 2.4665 and 2.5699. If the value of the test statistic is in the rejection region, we reject the null hypothesis. 2.5699 is less than 4.31, hence we reject the null hypothesis.

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