Armandy Discount Stores is a large department store catering primarily to low-income people. More than 20,000 different products are kept in inventory and sold by the store. Management has followed the practice of using the retail inventory method in previous years. A team of outside professional counters came into the store after closing and took a complete physical count of units and prices at retail by the use of tape recorders. The information on the tape recorders was then keypunched. The inventory value at retail was determined by means of the computer. Additional calculations were made to convert the retail inventory to cost. Management feels that this entire process is more costly than is desirable, considering the need to have staff members of the CPA firm involved at every step.

A partner in the CPA firm believes it may be possible to use statistical sampling to determine the inventory value at cost. Further discussion with Armandy’s management indicates that no perpetual records exist, but all merchandise purchases are computerized at the time of acquisition, including product description and unit cost. The decision is made to use a line item on the product-description computer output list as the sampling unit for mean- per-unit estimation. There are 24,856 lines on the list.

The recorded value of last year’s inventory was \($1,852,627.\) The audit partner and management decide they are willing to accept the point estimate as the recorded value if it is within \($75,000\) of the true value. They do not want more than a 5% risk that it is misstated by more than \($75,000\). Based on last year’s recorded inventory, the standard deviation is estimated as \($55\).

Required :

a. Evaluate the use of unstratified mean-per-unit estimation in this situation. What other alternatives should be considered ?

b. Evaluate the decision to use line items on the product-description computer output list as the sampling unit. What problems is the auditor likely to encounter ?

c. Should interval estimation or hypothesis testing be used in this situation? Explain.

d. Calculate the appropriate sample size, given the information provided to this point.

e. For approximately 10% of the items included in the random sample, there was no actual inventory on hand. How should these items be included in (or excluded from) the statistical results ?

f. Assume that a random sample of 1,100 items was selected. The total value of the inventory at historical cost was \($87,203\). The total of the individual values squared was \($9,871,405\). Calculate the confidence interval for the population. Is an adjusting entry appropriate at this point ? If so, state what the entry should be. If not, what action is necessary ?