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 - Basic Skills and Concepts: 15

Answer

μ is between -6.59 and 7.39. The result suggests that the method is not too effective because the interval contains 0.

Work Step by Step

$\alpha=1-0.98=0.02.$ $\sigma$ is 21, hence we use the z-distribution with $df=sample \ size-1=49-1=48$ in the table. $z_{\alpha/2}=z_{0.01}=2.33.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=2.33\cdot\frac{21}{\sqrt{49}}=6.99.$ Hence the confidence interval:$\mu$ is between 0.4-6.99=-6.59 and 0.4+6.99=7.39. The result suggests that the method is not too effective because the interval contains 0.
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