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: 8

Answer

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{8632.5^2}{7301.2^2}=1.398.$ The critical values by the table with df=min(187,209)=187: $f_{0.05}$ is between 1 and 1.3519. the corresponding probability using the table, hence P=0.1081070292. If the value of the test statistic is in the rejection region, reject the null hypothesis. 1.398 is more than 1.3519, hence we reject the null hypothesis. The number of words spoken by men varies more than the women's.
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