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: 38

Answer

μ is between 22.91 and 24.99.

Work Step by Step

Given mean:23.95. Given $\sigma$:2.55. $\alpha=1-0.98=0.01.$ $\sigma$ is known, hence we use the z-distribution using the table. $z_{\alpha/2}=z_{0.005}=2.58.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=2.58\cdot\frac{2.55}{\sqrt{40}}\approx1.04.$ Hence the confidence interval:$\mu$ is between 23.95-1.04=22.91 and 23.95+1.04=24.99.
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