Question

1. Goodness of Fit Problem: According to Benford’s Law, the leading digits in a set of data should follow the distribution in the table below. An auditor of a company finds the distribution of leading digit, also given in the table below. Is there evidence that the leading digits of the company differs from Benford’s Law enough to make the auditor suspicious that the books have been fixed

Leading Digit 1 2 3 4 5 6 7 8 9
Benford’s Law 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6%
# of Leading 800 400 350 300 280 250 200 180 150

Answer 1

Yes, there is evidence that the leading digits of the company differ from Benford’s Law, as the observed distribution does not align with the expected distribution, raising suspicion about the accuracy of the company's records.

Benford's Law states that in many naturally occurring datasets, the leading digits tend to follow a specific distribution. The expected distribution of leading digits according to Benford's Law is provided in the table you've given. The auditor of the company has compared this expected distribution with the observed distribution of leading digits in the company's data.

In this case, the observed distribution of leading digits in the company's data is presented in the second row of the table. The numbers of leading digits for each digit from 1 to 9 are provided. To assess whether the company's data aligns with Benford's Law, the auditor needs to compare the expected percentages from Benford's Law with the observed percentages in the company's data.