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 - Page 357: 12


μ is between 22.858 and 25.042.

Work Step by Step

$\alpha=1-0.99=0.01.$ $\sigma$ is known(2.55), hence we use the z-distribution with $df=sample \ size-1=40-1=39$ in the table. $z_{\alpha/2}=t_{0.005}=2.708.$ Margin of error:$z_{\alpha/2}\cdot\frac{s}{\sqrt {n}}=2.708\cdot\frac{2.55}{\sqrt{40}}=1.092.$ Hence the confidence interval:$\mu$ is between 23.95-1.092=22.858 and 23.95+1.092=25.042. We are 99% confident that the mean falls within the confidence interval of chocolate chips.
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