A delivery truck manager takes a sample of 25 delivery trucks and calculates the

Question

A delivery truck manager takes a sample of 25 delivery trucks and calculates the sample mean and sample standard deviation for the cost of operation. A 95% confidence interval for the population mean cost is constructed and found to be $253 to $320. He reasons that this interval contains the mean operating cost for the entire fleet of delivery trucks since the sample mean is contained in this interval.

a. Do you agree with his reasoning?

b. How would you interpret this confidence interval?

c. Is this an appropriate use of a confidence interval?

d. Concerning your answers to parts a through c, what assumptions did you make (if any)? Does the Central Limit Theorem apply? Why or why not?

e. How does this apply or could apply to your profession?

Explanation / Answer

Solution:-

a.   I do not agree with this reasoning because sample mean will always be in the confidence interval, but it does not ensure that the population mean will be in that interval.

b.   With 95% confidence level, population mean lies in the confidence interval. That means if we build 100 different confidence intervals with 100 different datasets for the same purpose then 95 out of 100 confidence intervals will contain true population mean. So, with 95% confidence level, true mean operating cost will be within $253 and $320.

c. Objective of a confidence interval is to understand the population parameter with certain confidence. Here, our objective is to understand the mean operating cost for the fleet of delivery trucks. Yes, this can be considered as appropriate use but, the interpretation of the confidence interval is not proper.

d. If we have information on monthly expenditure on food for several families of similar types (assuming same family size). Then we can construct a 95% confidence interval for average spending on food for a given month. We can leverage this information for monthly budget planning.

e. Consider the following scenario. In a production house, we are measuring number defective items produced in a particular shift (Assuming number of items produced in a shift is fixed). Then we cssan build a confidence interval for number of defective items in a shift. In a certain shift, if the numbers of defective items exceed the confidence band, which is unusual, then we can stop the production and can take some corrective action. Thus with the help of confidence interval we can easily detect the malfunctioning of the system and can reduce the production and labor costs.

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