Question: Evaluating a Sampling Application. Tom Barton, an assistant accountant with a local CPA firm, recently graduated from Other University. He studied statistical sampling for auditing in college and wants to impress his employers with his knowledge of modern auditing methods. Barton decided to select a random sample of payroll checks for the test of controls using a tolerable rate of deviation of 5 percent and an acceptable risk of overreliance of 5 percent. The senior accountant told Barton that 2 percent of the checks audited last year had one or more errors in the calculation of net pay. He decided to audit 100 random checks. Because supervisory personnel had paychecks with higher amounts than production workers, he selected 60 of the supervisor checks and 40 checks of the others. He was very careful to see that the selections of 60 from the April payroll register and 40 from the August payroll register were random. The audit of this sample yielded two deviations, exactly the 2 percent rate experienced last year. The first was the deduction of federal income taxes based on two exemptions for a supervisory employee whose W-4 form showed four exemptions. The other was payment to a production employee at a rate for a job classification one grade lower than it should have been. The worker had been promoted the week before, and Barton found that in the next payroll he was paid at the correct (higher) rate.

When he evaluated this evidence, Barton decided that these two findings were really not control deviations at all. The withholding of too much tax did not affect the expense accounts and the proper rate was paid the production worker as soon as the clerk caught up with the change orders. Barton decided that having found zero deviations in a sample of 100, the upper limit rate of deviation at 5 percent risk of overreliance was 3 percent, which easily satisfied his predetermined criterion. The senior accountant was impressed. Last year he had audited 15 checks from each month and Barton's work represented a significant time savings. The reviewing partner on the audit also was impressed because she had never thought that statistical sampling could be so efficient, and that was the reason she had never studied the method.

Required: Identify and explain the mistakes made by Barton.