As an example of a situation in which several different statistics could reasona

Question

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 ninvoices and determining the audited (correct) value for each one. Suppose that the sample gives the following results (in dollars).

52

Let

Y

X

D

X

D

X / Y

Invoice 1 2 3 4 5 Book value 323 715 542 187 127 Audited value     323 511 542 187 179 Error 0 204 0 0

52

Explanation / Answer

If N=5000 and T=1,761,300 then the corresponding point estimates are

So Estimated total audited value X = $ (5000*348.4)= $ 1,742,000

D= (0+204+0+0-52)/5 =30.4

So the estimateed total audit value = T-ND=$ (1,761,300-5000*30.4)=$ 1,609,300

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