Elementary Statistics (12th Edition)

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

Chapter 7 - Estimates and Sample Sizes - 7-3 Estimating a Population Mean - Beyond the Basics: 36

Answer

μ is between 0.491 and 0.947.

Work Step by Step

Given mean:0.719. Given $\sigma$:0.366. $\alpha=1-0.9=0.1.$ $\sigma$ is known, hence we use the z-distribution using the table. $z_{\alpha/2}=z_{0.05}=1.645.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=1.645\cdot\frac{0.366}{\sqrt{7}}=0.228.$ Hence the confidence interval:$\mu$ is between 0.719-0.228=0.491 and 0.719+0.228=0.947.
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