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: 17

Answer

μ is between 6.35 and 16.37. The population is all daily receipts of the movie. A problem can be that it is a convenience sample and hence we cannot deduct anything to the population.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{58+22+...+4}{14}=16.36.$ Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(58-16.36)^2+...+(4-16.36)^2}{13}}=14.52.$ $\alpha=1-0.99=0.01.$ $\sigma$ is 16.36, hence we use the z-distribution with $df=sample \ size-1=14-1=13$ in the table. $z_{\alpha/2}=z_{0.005}=2.58.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=2.58\cdot\frac{14.52}{\sqrt{14}}=10.01.$ Hence the confidence interval:$\mu$ is between 16.36-10.01=6.35 and 16.36+10.01=16.37. The population is all daily receipts of the movie. A problem can be that it is a convenience sample and hence we cannot deduct anything to the population.
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