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 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 , and the last involving T and / . If N 5000 and T 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.)