Benford's law, also called first-digit law, describes that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way shown in the following table.
Leading Digit 1 2 3 4 5 6 7 8 9
Distribution of Leading Digit (%) 30.1 17.6 12.5 9.7 7.9 6.7 5.8 5.1 4.6
The owner of a small business would like to audit its accounts payable over the past year because of a suspicion of fraudulent activities. He suspects that one of his managers is issuing checks to non-existing vendors in order to pocket the money. There have been 790 checks written out to vendors by this manager. The leading digits of these checks are listed as follow:
Leading Digits 50 15 12 74 426 170 11 23 9
Suppose you are hired as a forensic accountant by the owner of this small business, what statistical test would you employ to determine if there is fraud committed in the issuing of checks? What is the test statistic in this case?