As an example of a situation in which several different statistics could reasonably be used to calculate a point estimate, consider a population of N invoices. Associated with each invoice is its "book value," the recorded amount of that invoice. Let T denote the total book value, a known amount. Some of these book values are erroneous. An audit will be carried out by randomly selecting n invoices and determining the audited (correct) value for each one. Suppose that the sample gives the following results (in dollars).

Let
= sample mean book value
= sample mean audited value
D = sample mean error
Propose three different statistics for estimating the total audited (i.e., correct) value-one involving just N and , another involving T, N, and D, and the last involving Ï„ and /. If N 5 5000 and Ï„ 5 1,761,300, calculate the three corresponding point estimates. (The article "Statistical Models and Analysis in Auditing," Statistical Science, 1989: 2-33 discusses properties of these estimators.)

Invoice Book value Audited value 300 520 526 200 157 Error 300 720 526 200 127 0 200 0 -30