Baker, CPA, was engaged to audit Mill Company's financial statements for the year ended September 30, 20X1. After obtaining an understanding of Mill's internal control structure, Baker decided to obtain evidential matter about the effectiveness of both the design and operation of the policies and procedures that may support a low assessed level of control risk concerning Mill's shipping and billing functions. During the prior years' audits Baker used nonstatistical sampling, but for the current year Baker used a statistical sample in the tests of controls to eliminate the need for judgment.

Baker wanted to assess control risk at a low level, so a tolerable rate of deviation or acceptable upper precision limit (UPL) of 20 percent was established. To estimate the population deviation rate and the achieved UPL, Baker decided to apply a discovery sampling technique of attribute sampling that would use a population expected error rate of 3 percent for the 8,000 shipping documents, and decided to defer consideration of allowable risk of assessing control risk too low (risk of overreliance) until evaluating the sample results. Baker used the tolerable rate, the population size, and the expected population error rate to determine that a sample size of 80 would be sufficient. When it was subsequently determined that the actual population was about 10,000 shipping documents, Baker increased the sample size to 100.

Baker's objective was to ascertain whether Mill's shipments had been properly billed. Baker took a sample of 100 invoices by selecting the first 25 invoices from the first month of each quarter. Baker then compared the invoices to the corresponding prenumbered shipping documents.

When Baker tested the sample, eight errors were discovered. In addition, one shipment that should have been billed at $10,443 was actually billed at $10,434. Baker considered this $9 to be immaterial and did not count it as an error.

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

Required

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