Audit Working Papers 1

AUDIT RISK

What If You Were an Orange Inspector?

Please imagine that you have just taken a job as an Orange inspector for Best Orange (Pty) Limited. —a large Orange grower. You are replacing a previous inspector who was recently fired for lack of due care, and your new employer has made it clear that you must meet high performance standards to make it through your probationary period. Best Oranges owns and operates many Orange orchards and sells its Oranges to major fruit processors (hereafter "buyers") whose prod­ucts include fresh Oranges, Orange sauce, and Orange juice. Best Orange makes large shipments of Oranges to buyers on a daily basis during harvest season; each shipment contains approximately 1,500 bushels from various orchards. Each bushel contains 100 to 150 Oranges. The bushel indicates which orchard the Oranges come from. Your job is to manually inspect the quality of Oranges just prior to shipment. Obviously, there is neither the time nor need to inspect every Orange, so you will examine a sample of Oranges.

Imagine it is your first day on the job; consider for a moment what infor­mation about the Oranges, your employer, or the buyer you would like to know before you begin your inspections. Among other things, it would be useful to know the answers to the following questions:

• ·         For what purpose will the current shipment be used (e.g., fresh Oranges, sauce, or juice)?
• ·         The definition of a defect—what constitutes a bad Orange?
• ·    Tolerable defect percentage—what percentage of defective Oranges will the buyers accept in a shipment?
• ·         What has Best Orange's historical defect percentage been?
• ·         Have growing conditions (e.g., weather, pests) been normal this year?
• ·         What happens if we send a shipment that contains an unacceptably high percentage of defects?
• ·         Level of assurance or confidence—how confident do I need to be in my testing results?
• ·         What quality controls and processes does Best Oranges have in place?
• ·         Are the defect percentages the same for all orchards?

Suppose you receive satisfactory answers to these questions and you begin your testing. The primary purpose of sampling is to draw inferences about the whole population based on the results of testing only a subset of the population. You draw a sample of 20 Oranges and find 1 defective Orange. Projecting your sample defect rate to the total population suggests a shipment defect rate of 5 percent (1/20). While 5 percent is your best estimate based on your sample results, will you be positive that you have determined the correct defect rate for the entire shipment? The obvious answer is no, because there is a chance the shipment defect rate could be higher or lower than your sample rate of 5 percent. The uncertainty associated with sampling is known as sampling risk. Whenever inspectors or auditors test less than the entire population, there is a risk that the sample results will not be similar to what the results would be if the inspector were to test the entire population. In other words, sampling risk is the risk that the results of a sample are not representative of the population. 

Sampling theory allows us to measure the risk associated with sampling. For example, if we knew a buyer would accept up to 10 percent defective Oranges in a shipment, we can compute the risk that the actual shipment defect rate is higher than 10 percent (you will learn how to make such evaluations in this chapter). For a sample of 20 Oranges with 1 defective Orange there is approximately a 40 percent chance that the actual shipment defect rate exceeds the buyer's tolerable defect rate of 10 percent. Inspectors and auditors can reduce sampling risk by taking larger samples. In the extreme, if you tested 100 percent of the Oranges in the shipment, then there would be no sampling risk because you would know with certainty the true shipment defect rate. While it would not be economical for you to inspect every Orange, you could increase your sample size to reduce the risk that the shipment will contain an unacceptably high rate of defects. If you examine a sample of 100 Oranges and find 5 defects, sampling theory indicates that you would only face approximately a 6 percent chance that the true shipment defect rate exceeds the buyer's tolerable rate of 10 percent. So an important concept in audit sampling is that by increasing sample size, you can reduce uncertainty and risk.