You desire to evaluate the reasonableness of the book value of the inventory of your client, Draper, Inc. You satisfied yourself earlier as to inventory quantities. During the examination of the pricing and extension of the inventory, the following data were gathered using appropriate unrestricted random sampling with replacement procedures:

Required:

a. Based on the sample results, what is the estimate of the total value of the inventory? Show computations in good form where appropriate.

b. What statistical conclusion can be reached regarding the estimated total inventory value calculated in

a. above at the confidence level of 95 percent? Present computations in good form where appropriate.

c. Independent of your answers to

a. and b., assume that the book value of Draper's inventory is \(\$ 1,700,000\), and based on the sample results the estimated total value of the inventory is \(\$ 1.69\) million. The auditor desires a confidence (reliability) level of 95 percent. Discuss the audit and statistical considerations the auditor must evaluate before deciding whether the sampling results support acceptance of the book value as a fair presentation of Draper's inventory.

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1. Total items in the inventory (N) 2. Total items in the sample (n) 3. Total audited value of items in the sample 400 4. (x, x) 5. Formula for estimated population standard de- viation 6. Formula for estimated standard error of the mean Sx 12,700 400 $38,400 $312,816 31 (x) - x) 12- SE 7. Confidence level coefficient of the standard error of the mean at a 95 percent confidence (reliability) level = 1 Sxj n 1.96