Question: In accounting and auditing, the following sampling method is sometimes used to estimate a population total. In estimating the value of an inventory, suppose that a book value exists for each item and is readily accessible. For each item in the sample, the difference D, audited value minus book value, is determined. The inventory value is estimated by the sum of the book values of the population and N D, where N is the population size.

a. Show that the estimate is unbiased.

b. Find an expression for the variance of the estimate.

c. Compare the expression obtained in part (b) to the variance of the usual estimate, which is the product of N and the average audited value. Under what circumstances would the proposed method be more accurate?

d. How could a ratio estimate be employed in this situation? Would there be any advantage or disadvantage to using a ratio estimate rather than the proposed method?