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 474: 7


a) -11.6 b)17.2134 c)-1.507 d)$\pm 2.776$

Work Step by Step

a) The differences: 22-44=-22, 37-41=-4, 28-62=-34, 63-52=11, 32-41=-9. $\overline{d}$ is the averages of the differences, hence: $\overline{d}=\frac{-22-4-34+11-9}{5}=-11.6.$ b)$s_d$ is the standard deviation of the differences, hence$s_d=\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(-22+11.6)^2+(-4+11.6)^2+(-34+11.6)^2+(11+11.6)^2+(-9+11.6)^2}{4}}=17.2134.$ c) The test statistic is:$t=\frac{\overline{d}-\mu_d}{s_d/\sqrt{n}}=\frac{-11.6-0}{17.2134/\sqrt{5}}=-1.507.$ d) The corresponding critical value using the table with df=5-1=4: $\pm t_{\alpha/2}=\pm t_{0.025}=\pm 2.776.$
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