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: 37

Answer

μ is between 6132 and 19664.

Work Step by Step

Given mean:12898. Given $\sigma$:7718.8. $\alpha=1-0.95=0.05.$ $\sigma$ is known, hence we use the z-distribution using the table. $z_{\alpha/2}=z_{0.025}=1.96.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=1.96\cdot\frac{7718.8}{\sqrt{5}}\approx6766.$ Hence the confidence interval:$\mu$ is between 12898-6766=6132 and 12898+6766=19664.
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