Mary Obrien, CPA, is using stratified mean-per-unit to determine whether the client’s recorded inventory is correctly stated. The decision has been made to use mean-per-unit rather than difference or ratio estimation because a low error rate is expected.

Inventory has been stratified by two criteria: inventory location, and the recorded value of individual inventory items. There are six strata and three inventory locations.

The audit tests for a sample item include comparing the recorded count to the perpetual record at the balance sheet date, comparing the perpetual record on the audit date to the inventory on hand, testing the unit costs by reference to vendors’ invoices, and extending the price times quantity. The client did not take a physical at year-end, but inventory is counted annually and the records are considered excellent. No adjusting entries are likely to be accepted by the client unless a large error is discovered.

The following information is available from the accounting records and estimates of the population data:

The following specifications are set:

Required:

a. Calculate the total required sample, using the optimum allocation method. Use the finite correction factor where it is appropriate.

b. Allocate the total sample size in a to each stratum in proportion to the recorded value.

c. Suggest two ways the auditor might have designed the strata to have a smaller required sample size and still meet the audit requirements. What problems could exist for each way suggested ?

d. Assume Mary calculated the required sample size in a and allocated the sample to the strata in part b. She decided to use the following sample size and ended up with the following results after performing all audit tests. Calculate the confidence limits for the inventory valuation.

e. Evaluate the acceptability of the population, using the appropriate decision rule.

f. Mary is considering two alternatives at this point:
(i) Divide one of the strata into two strata and recalculate the results without changing the sample size.
(ii) Increase the sample size in one stratum.
Evaluate each of these two alternatives. If she decides to follow one of these two approaches, which stratum should she take? Explain your answer.

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Stratum Population size Recorded value Estimated standard deviation 123456 600 $ 300,000 750 3,500 800,000 500 800 400,000 400 2,900 450,000 300 500 500,000 1,200 4,700 700,000 200 13,000 $3,150,000