Essentials of Statistics (5th Edition)

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

Chapter 7 - Estimates and Sample Sizes - 7-3 Estimating a Population Mean: 10

Answer

$\mu$ is between 0.45 and 0.988

Work Step by Step

$\alpha=1-0.9=0.1.$ $\sigma$ is not known, hence we use the t-distribution with $df=sample \ size-1=7-1=6$ in the table. $t_{\alpha/2}=t_{0.05}=1.943.$ Margin of error:$t_{\alpha/2}\cdot\frac{s}{\sqrt {n}}=1.943\cdot\frac{0.366}{\sqrt{7}}=0.269.$ Hence the confidence interval:$\mu$ is between 0.719-0.269=0.45 and 0.719+0.269=0.988
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