Essentials of Statistics (5th Edition)

Published by Pearson
ISBN 10: 0-32192-459-2
ISBN 13: 978-0-32192-459-9

Chapter 8 - Hypothesis Testing - 8-4 Testing a Claim about a Mean - Page 416: 25

Answer

There is sufficient evidence to support that the mean magnitude is more than 1.

Work Step by Step

$H_{0}:\mu=1$. $H_{a}:\mu <1.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{1.1842-1}{0.5873/\sqrt{50}}=2.218.$ The P-value is the interval of probabilities between which the value of the test-statistic lies in the table with degree of freedom=sample size-1=50-1=49, hence P is between 0.01 and 0.025. 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 less than $\alpha=0.05$, because it is less than 0.025, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the mean magnitude is more than 1.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.