5. 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 Y
sample mean book value X
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 X, another involving T, N, and D, and the last involving T and X/Y . 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.)