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).

Invoice 1 2 3 4 5 Book value 300 720 526 200 127 Audited value 300 520 526 200 157 Error 0 200 0 0 30 Let

 sample mean book value

 sample mean audited value

 sample mean error Several different statistics for estimating the total audited (correct) value have been proposed (see Statistical Models and Analysis in Auditing, Statistical Sci., 1989: 2—33). These include Mean per unit statistic  N Difference statistic  T  N Ratio statistic  T #

If N  5000 and T  1,761,300, calculate the three corresponding point estimates. (The cited article discusses properties of these estimators.)