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: 16

Answer

μ is between 74.26 and 125.54. The result suggests that the mean wakeup time is likely because it is in the interval and that zopi-cloning doesn't seem to be effective, because it is not more then the upper bound.

Work Step by Step

$\alpha=1-0.98=0.02.$ $\sigma$ is 42.3, hence we use the z-distribution with $df=sample \ size-1=16-1=15$ in the table. $z_{\alpha/2}=z_{0.01}=2.33.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=2.33\cdot\frac{42.3}{\sqrt{16}}=24.64.$ Hence the confidence interval:$\mu$ is between 98.9-24.64=74.26 and 98.9+24.64=125.54. The result suggests that the mean wakeup time is likely because it is in the interval and that zopi-cloning doesn't seem to be effective, because it is not more then the upper bound.
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