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: 20

Answer

μ is between 28.4 and 38.8.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{32+32+...+25}{15}=33.6.$ Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(32-33.6)^2+...+(25-33.6)^2}{14}}=7.67.$ α=1−0.98=0.02. σ is 7.67, hence we use the z-distribution with df=sample size−1=15−1=14 in the table. $z_{\alpha/2}=z_{0.01}=2.33.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=2.33\cdot\frac{7.67}{\sqrt{15}}=5.2.$ Hence the confidence interval:μ is between 33.6-5.2=28.4 and 33.6+5.2=38.8.
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