Elementary Statistics (12th Edition)

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

Chapter 9 - Inferences from Two Samples - 9-4 Two Dependent Samples (Matched Pairs) - Basic Skills and Concepts - Page 475: 14


Reject the null hypothesis.

Work Step by Step

$H_{0}:\mu_d=0,$ $H_{a}:\mu_d\ne0$. The test statistic is:$t=\frac{\overline{d}-\mu_d}{s_d/\sqrt{n}}=\frac{-72.2-0}{9.3113/\sqrt{5}}=-17.339.$ The P is the corresponding probability using the table with df=5-1=4, 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 lessthan $\alpha=0.01$, hence we reject the null hypothesis. Hence the measurements from the two arms seem to be a bit different.
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