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: 13

Answer

μ is between 98.08 and 98.32. The result suggets that the mean of the body temperature is less than 98.6.

Work Step by Step

$\alpha=1-0.95=0.05.$ $\sigma$ is 0.62, hence we use the z-distribution with $df=sample \ size-1=106-1=105$ in the table. $z_{\alpha/2}=t_{0.025}=1.96.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=1.96\cdot\frac{0.62}{\sqrt{106}}=0.12.$ Hence the confidence interval:$\mu$ is between 98.2-0.12=98.08 and 98.2+0.12=98.32. The result suggets that the mean of the body temperature is less than 98.6.
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