As an example of a situation in which several differentstatis tics could reasonably be

Chapter 6, Problem 5

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As an example of a situation in which several differentstatis tics could reasonably be used to calculate a pointestimate, consider a population of N invoices. Associatedwith each invoice is its book value, the recordedamount 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 ninvoices and determining the audited (correct) value foreach one. Suppose that the sample gives the followingresults (in dollars).LetY 5 sample mean book valueX 5 sample mean audited valueD 5 sample mean errorPropose three different statistics for estimating thetotal audited (i.e., correct) valueone involving justN and X, another involving T, N, and D, and the lastinvolving T and XyY. If N 5 5000 and T 5 1,761,300,calculate the three corresponding point estimates. (Thearticle Statistical Models and Analysis in Auditing,Statistical Science, 1989: 233 discusses properties ofthese estimators.)