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: 19

Answer

μ is between 0.7282 and 1.1482. 1.6 is more than the upper bound of the interval, hence the radiation must be 1.6 or less.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{0.38+0.55+...+1.46}{11}=0.9382.$ Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(0.38-0.9382)^2+...+(1.46-0.9382)^2}{10}}=0.4229.$ α=1−0.9=0.1. σ is 0.4229, hence we use the z-distribution with df=sample size−1=11−1=10 in the table. $z_{\alpha/2}=z_{0.05}=1.645.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=1.645\cdot\frac{0.4229}{\sqrt{11}}=0-21.$ Hence the confidence interval:μ is between 0.9382-0.21=0.7282 and 0.9382+0.21=1.1482. 1.6 is more than the upper bound of the interval, hence the radiation must be 1.6 or less.
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