Part 2 Dr. Frank Benford, a physicist at General Electric in the 1920s, found that the first and second digits of many populations of numbers occur with a fairly consistent frequency. This has been found true, for example, of census numbers and certain accounting populations, such as accounts payable. Benford developed a model that predicted the frequency of each digit occurring in a particular location depending on the length of a number. For example, he found that the digit #1 occurs as the first digit in about 30% of all populations, while the digit #2 occurs in about 17.5% of all populations. On the other hand, the digit #9 occurs as the first digit only about 4.5% of the time. Thus, digits such as 990 do not occur as often as digits such as 124. Many other researchers have empirically verified the Benford predictions. Auditors have found that as individuals commit fraud or make up fraudulent transactions, their intuition in developing numbers for the fake documents often does not follow Benfords Law. Therefore, auditors have come to use Benfords Law to identify a wide variety of unusual transactions, including fraud, double payments, and other fictitious accounts. Audit software, such as ACL, comes with modules that allow auditors to apply Benfords Law to search for unusual patterns in populations by identifying numbering patterns that diff er signifi cantly from that predicted by Benfords Law. Benford Analysis can be found by clicking Analysis | Perform Benford Analysis. You will be instructed to select a field on which to perform the analysis. You can then make a choice to perform an analysis on the leading digit only, or you can perform an analysis on the two leading digits. You can choose the type of output you want for the analysis by clicking the Output tab at the top of the window. The GRAPH option will provide a bar graph with the predicted and actual frequencies of each leading digit or the two leading digits. The SCREEN and FILE options will create a report containing the following: The actual count of the leading digit (or two leading digits) The expected count of the digit(s) A Zstat statistic The Zstat statistic is derived from the probability of the deviation between the actual count and the expected count of the digit. The signifi cance of the Zstat statistic is determined by comparing it with the Z statistic used to describe normal distributions in most statistical textbooks. For example, there is a 95% chance that most samples from a distribution would fall within 1.96 standard deviations from the mean, thus creating a Zstat of 1.96 for a 5% tail end of a distribution and 2.58 for a 1% tail. Any Zstat statistic greater than 2.58 would indicate a very rare occurrence. To illustrate the power of Benfords Law in an auditing context, assume that you are the internal auditor for Knot Manufacturing Company and are auditing the travel, entertainment, and meal reimbursements for 2013. Company policy requires receipts and managements approval of all reimbursements over $5,000. Download the file Expense Reimbursements excel file. Analyze expense reimbursements using Benfords Law and ACL. Import the Expense Reimbursements file, which contains the reimbursement document numbers, employee numbers, and the amount of each reimbursement. Click Analyze | Perform Benford Analysis for the AMOUNT of the reimbursement. 1. Analyze on the leading digit. Choose Output to Screen and again to Graph. Take a screenshot of both outputs. (5 marks) 2. Analyze on the leading two digits. Choose Output to Screen and again to Graph. Take a screenshot both outputs. (5 marks) 3. Summarize the number and amount of reimbursements between $4,900 and $5,000 by employee number. Take a screenshot of the results (10 marks). 4. Analyze the results and provide possible explanations for the results. Identify reimbursements for certain employees that may need further investigation. (10 marks)