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: 21

Answer

μ is between 6.43 and 15.67. The population mean doesn't seem to be less than 7, because 7 is in the confidence interval.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{3+6.5+...+17.5}{10}=11.05.$ Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(3-11.05)^2+...+(17.5-11.05)^2}{9}}=6.46.$ α=1−0.95=0.05. σ is 6.46, hence we use the z-distribution with df=sample size−1=10−1=9 in the table. $z_{\alpha/2}=z_{0.025}=1.96.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=1.96\cdot\frac{6.46}{\sqrt{10}}=4.62.$ Hence the confidence interval:μ is between 11.05-4.62=6.43 and 11.05+4.62=15.67. The population mean doesn't seem to be less than 7, because 7 is in the confidence interval.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.