When conducting an audit, accountants check invoices by drawing random samples for inspection. In one case, the accountants failed to include any of 17 fraudulent invoices in their sample of 100 invoices. When the company collapsed after the accountants had certified its financial statements, a creditor who had relied on the reports sued, claiming that the accountants had been negligent. The probability that none of the 17 invoices would be included in a random sample of 100 if there were 1,000 invoices in all equals 0.16. Is there sufficient evidence to justify holding the accountants liable for failing to draw a larger sample?
In the first case, the accountant missed to include any of 17 fraudulent invoices in the large sample of 100 invoices and a random sample of 100, and there is a very less probability that none of the 17 invoices is included. If there were 1000 invoices in total, then it equals to 0.16. Hence, the conclusion is that out of a hundred, 16 times, fraudulent invoices would not be included in the sample. The probability that perhaps all the 17 invoices are included in sample= 1-.16= .84, which is a very high probability. In case the result samples are excluded, and fraudulent invoices are included, then the account should collect a large sample. There is sufficient evidence to justify the fact that accountants were liable for failing to draw a larger sample.