Elementary Statistics (12th Edition)

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

Chapter 9 - Inferences from Two Samples - 9-5 Two Variances or Standard Deviations - Basic Skills and Concepts: 17

Answer

Fail to reject the null hypothesis.

Work Step by Step

$H_{0}:\sigma_1=sigma_2,$ $H_{a}:\sigma_1\ $ is more than $ \sigma_2$. :$F=\frac{s_1^2}{s_2^2}=\frac{20.6882^2}{18.5821^2}=1.2468.$ The critical values by the table with df=min(39,39)=39: $f_{0.05}$ is between 1.6928 and 1.8409. If the value of the test statistic is in the rejection region, reject the null hypothesis. 1.2468 is less than 1.8409, hence we fail to reject the null hypothesis.
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