Essentials of Statistics (5th Edition)

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

Chapter 9 - Inferences from Two Samples - 9-4 Two Dependent Samples (Matched Pairs) - Page 471: 25

Answer

Reject the null hypothesis.

Work Step by Step

$H_{0}:\mu_d=6.8,$ $H_{a}:\mu_d\ne6.8$. The test statistic is:$t=\frac{\overline{d}-\mu_d}{s_d/\sqrt{n}}=\frac{1.1791-6.8}{3.8883/\sqrt{67}}=-11.833.$ The P is the corresponding probability using the table with df=67-1=66, hence P is less than 0.01. 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$\alpha=0.05$, hence we reject the null hypothesis. Hence the differences don't seem to be 6.8.
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