The Chesapeake and Ohio Freight Study 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 Can relatively small samples is time consuming and costly. If the actually provide results that are division of total revenue to the nearly as accurate as those railroads could be done accurately obtained from a census? on the basis of a sample-as Statisticians have proven that such statisticians contend-considerable is the case, but a real study with savings could be realized in sample and census results can be accounting and clerical costs. enlightening. To convince themselves of the When a freight shipment travels validity of the sampling approach, over several railroads, the revenue officials of the Chesapeake andOhio Railroad Company (C&O) sampled. For each waybill in the undertook a study of freight sample, the amount of freight shipments that had traveled over its revenue due C&O was calculated Pere Marquette district and another and, from those amounts, the total railroad during a 6-month period. revenue due C&O was estimated to The total number of waybills for that be $64,568. period (22,984) and the total freight How close was the estimate revenue were known. of $64,568, based on a sample of The study used statistical theory only 2072 waybills, to the total to determine the smallest number of revenue actually due C&O for the waybills needed to estimate, with a 22,984 waybills? Take a guess! We'll prescribed accuracy, the total freight discuss the answer at the end of this revenue due C&O. In all, 2072 of the chapter. 22,984 waybills, roughly 9%, wereAt tlte beginning of this chapter. we discussed a freight study commissioned by the Chesapeake and Ohio Railroad Com- pan).l (C650). A sample of 20?? waybills from a population of 22.984 wayhills was Used to estimate the total revenue due (2&0. The estimate arrived at was $64,563. Because all 22,984 waybills were available. a census could be taken to determine exactly.r the total revenue due (3&0 and thereby reveal the accuracy of the estimate obtained by sampling. The ex act amount due l[3&0 was found to be $64.65 | . CASE STU DY DISCUSSION THE CHESAPEAKE AND OHIO FREIGHT STUDY What percentage of the waybills constituted the sample? b. What percentage error was made by using the sample to esti- Ill. mate the total revenue due (3&0? At the time of the study. the cost of a census Was approxi- mately $5000. whereas the cost for [he sample estimate was only,' MINI]- Knowing this information and your answers to parts (a) and (b). do you think that sampling was preferable to a census?l Explain your answer. In the study. the $83 error was against C&0. Could the error have been in C&0's favor