Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 7 - Estimates and Sample Sizes - Review - Cumulative Review Exercises - Page 375: 5


μ is between 3.64 and 7.36.

Work Step by Step

$\alpha=1-0.95=0.05.$ $\sigma$ is not known, hence we use the t-distribution with $df=sample \ size-1=40-1=49$ in the table. $t_{\alpha/2}=t_{0.025}=2.023.$ Margin of error:$t_{\alpha/2}\cdot\frac{s}{\sqrt {n}}=2.023\cdot\frac{5.8}{\sqrt{40}}=1.86.$ Hence the confidence interval:$\mu$ is between 5.5-1.86=3.64 and 5.5+1.86=7.36.
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