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 - Page 483: 6

Answer

Fail to reject the null hypothesis.

Work Step by Step

$H_{0}:\sigma_1=sigma_2,$ $H_{a}:\sigma_1$ is more than $\sigma_2$: $F=\frac{s_1^2}{s_2^2}=\frac{3.67^2}{3.65^2}=1.010989.$ The P is the corresponding probability using the table, hence P=0.4745. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is more than $\alpha=0.05$, hence we fail to reject the null hypothesis. Hence the ages don't seem to have different standard deviations.
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