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: 35

Answer

$\mu$ is between 8.156 and 11.46.

Work Step by Step

Given mean:9.808. Given $\sigma$:5.013. $\alpha=1-0.98=0.02.$ $\sigma$ is known, hence we use the z-distribution using the table. $z_{\alpha/2}=z_{0.01}=2.33.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=2.33\cdot\frac{5.013}{\sqrt{50}}=1.652.$ Hence the confidence interval:$\mu$ is between 9.808-1.652=8.156 and 9.808+1.652=11.46.
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