Elementary Statistics (12th Edition)

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

Chapter 8 - Hypothesis Testing - 8-4 Testing a Claim About a Mean - Beyond the Basics: 30

Answer

There is not sufficient evidence to not support that the earthquakes don't have a mean depth of 10 kms.

Work Step by Step

$H_{0}:\mu=10$. $H_{a}:\mu \ne10.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{9.81-10}{5.01/\sqrt{50}}=-0.27.$ The P-value is the probability of z being less than -0.27 or bigger than 0.27 which is the sum of the probability of the z-score being less than -0.27 plus 1 minus the probability of the z-score being less than 0.27, hence:P=0.3936+1-0.7064=0.5028. 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 $\alpha=0.01$, because it is 0.5028, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to not support that the earthquakes don't have a mean depth of 10 kms.
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