Solved: Benfords law Faked numbers in tax returns, invoices, or expense account claims

QUESTION:

Benfords law Faked numbers in tax returns, invoices, or expense account claims often display patterns that arent present in legitimate records. Some patterns are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benfords law.3 Call the first digit of a randomly chosen record X for short. Benfords law gives this probability model for X (note that a first digit cant be 0): First digit: 1 2 3 4 5 6 7 8 9 Probability: 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 A forensic accountant who is familiar with Benfords law inspects a random sample of 250 invoices from a company that is accused of committing fraud. The table below displays the sample data. First digit: 1 2 3 4 5 6 7 8 9 Count: 61 50 43 34 25 16 7 8 6 (a) Are these data inconsistent with Benfords law? Carry out an appropriate test at the a = 0.05 level to support your answer. If you find a significant result, perform a follow-up analysis. (b) Describe a Type I error and a Type II error in this setting, and give a possible consequence of each. Which do you think is more serious?