Question: Can relatively small samples actually provide results that are nearly as accurate as those obtained from a census? Statisticians have proven that such is the case, but a real study with sample and census results can be enlightening. When a freight shipment travels over several railroads, the revenue from the freight charge is appropriately divided among those railroads. A waybill, which accompanies each freight shipment provides information on the goods, route, and total charges. From the waybill, the amount due each railroad can be calculated. Calculating these allocations for a large number of shipments is time consuming and costly. If the division of total revenue to the railroads could be done accurately on the basis of a sample—as statisticians contend—considerable savings could be realized in accounting and clerical costs. To convince themselves of the validity of the sampling approach, officials of the Chesapeake and Ohio Railroad Company (C&O) undertook a study of freight shipments that had traveled over its Pere Marquette district and another railroad during a 6-month period. The total number of waybills for that period (22,984) and the total freight revenue were known. The study used statistical theory to determine the smallest number of waybills needed to estimate, with a prescribed accuracy, the total freight revenue due C8

To reiterate, a sample of 2,072 waybills from a population of 22,984 waybills was used to estimate the total revenue due C&O. The estimate arrived at was $64,568.

Because all 22,984 waybills were available, a census could be taken to determine exactly the total revenue due C&O and thereby reveal the accuracy of the estimate obtained by sampling. The exact amount due C&O was found to be $64,651.

1. What percentage of the waybills constituted the sample?
2. What percentage error was made by using the sample to estimate the total revenue due C&O?
3. At the time of the study, the cost of a census was approximately $5000, whereas the cost for the sample estimate was $1000. Knowing this information and your answers to (a) and (b), do you think the sampling was preferable to the census? Explain you answer.
4. In the study, the $83 error was against C&O. Could the error have been in C&O’s favor?
5. This week, we learned about sampling distributions. Are there any applications from this week’s content to your major, your profession, or your interests? Please explain.

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document