The following is a set of sample and related data taken from a population of 1,000 items that have a recorded book value of \($498,000\). Even though only 20 items are used to simplify the problem, compute the sampling results as indicated.

Required :

a. Calculate each of the following:

b. Why is the computed precision interval so much smaller for difference than for mean-per-unit estimation ?

c. Convert the difference estimation confidence interval of the errors into a confidence interval of the audited values. Why is the point estimate different from that calculated under mean-per-unit estimation ?

d. Given the results in a, explain why an auditor would ever choose difference estimation rather than mean-per-unit, or vice versa.

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Sample data Sample Audited Book item no. amount amount Difference 123456780 $ 120 99 90 $ 100 $ 10 120 130 200 150 180 (20) 250 250 260 260 315 300 200 310 9 390 390 10 450 450 11 500 525 12 610 600 13 705 695 14 710 710 15 760 760 16 820 820 17 900 900 18 920 1,020 19 1,100 1,100 20 1,400 1,400 $10,830 $11,040 $210 | |||B||=| ||= (15)