# Chapter 7 - Estimates and Sample Sizes - 7-3 Estimating a Population Mean - Basic Skills and Concepts: 17

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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