Reference no: EM133341035

Case Study: Zhang, CPA, was engaged to audit Petrolite Company financial statements for the year ended September 30. After studying Petrolite's internal control, Zhang decided to obtain evidence about the effectiveness of both the design and operation of controls that may support a low assessed level of control risk concerning Petrolite's shipping and billing functions. During the prior years' audits, Zhang has used nonstatistical sampling, but for the current year Zhang used a statistical sample in the test of controls to eliminate the need for judgment.

Zhang wanted to assess control risk at a low level, so a tolerable deviation rate of 15% was established. To estimate the population deviation rate and the computed upper deviation rate, Zhang decided to apply an attribute sampling technique that would use an expected population deviation rate of 3% for the 8,000 shipping documents and to defer consideration of the allowable risk of assessing control risk too low (i.e., 1-desired confidence level) until the sample results were evaluated. Zhang used the tolerable deviation rate, the population size, and the expected population deviation rate to determine that a sample size of 80 would be sufficient. When it was subsequently determined that the actual population was 10,000 shipping documents, Zhang increased the sample size to 100.

Zhang's objective was to ascertain whether Petrolite's shipments were recognized as sales in the appropriate period. Zhang took a sample of 100 invoices by selecting the first 25 invoices from the first month of each quarter. Zhang then compared the invoices to the corresponding pre-numbered shipping documents.

When Zhang tested the sample, 8 deviations were discovered. Additionally, one shipment that should have been billed at $10,595 was actually billed at $10,959. Zhang considered this $364 to be immaterial and did not count it as an error.

In evaluating the sample results, Zhang made the initial determination that a 5% risk of assessing control risk too low (i.e., 95% confidence level) was desired and, using the appropriate statistical sampling table, determined that for eight observed deviations from the sample size of 100, the computed upper deviation rate was 14%. Zhang than calculated the allowance for sampling risk to be 5%, the difference between the actual sample deviation rate (8%) and the expected error rate (3%). Zhang reasoned that the actual sample deviation rate (8%) plus the allowance for sampling risk (5%) was less than the computed upper deviation rate (14%); therefore, the sample supported a lower level of control risk.

Question: Describe each incorrect assumption, statement, and inappropriate application of attribute sampling in Zhang's procedures.