Baker, CPA, was engaged to audit Mill Company's financial statements for the year ended December 31, 200X. After obtaining an understanding of Mill's internal control, Baker decided to obtain audit evidence about the effectiveness of both the design and operation of the controls that may support a low assessed level of control risk concerning Mill's shipping and billing functions. During the prior years' audits, Baker had used nonstatistical sampling, but for the current year Baker decided to use 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 of 20 percent was established. To estimate the population deviation rate and the achieved upper deviation rate, Baker decided to apply the discovery sampling method with an expected population deviation rate of 3 percent for the 8,000 shipping documents, and he decided to defer consideration of the risk of assessing control risk too low until the sample results had been evaluated. Baker used the tolerable 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 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 deviations were discovered. Additionally, 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 a deviation.

In evaluating the sample results, Baker made the initial determination that a reliability level of 95 percent (risk of assessing control risk too low of 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 upper deviation rate was 14 percent. Baker then calculated the allowance for sampling risk (5 percent), the difference between the actual sample deviation rate (8 percent), and the expected deviation 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 upper deviation rate (14 percent); therefore, the sample supported a low level of control risk.

Required:

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