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: 6

Answer

$\mu_d$ is between -2.7280538 and 2.8457008.

Work Step by Step

Null hypothesis:$\mu_d=0$, alternative hypothesis:$\mu_d$ is more than 0. The degree of freedom: 34-1=33. The corresponding critical value using the table: $t_{\alpha/2}=t_{0.05}=1.692.$ The margin of error: $E=t_{\alpha/2}\frac{s_d}{\sqrt{n}}=1.692\frac{9.604106}{\sqrt{34}}=2.7868773.$ Hence the confidence interval $\mu_d$ is between $\overline{d}-E$=0.0588235-2.7868773=-2.7280538 and $\overline{d}+E$=0.0588235+2.7868773=2.8457008.
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