According to Benford's Law, a Variety of Different Data Sets

question 18

Essay

According to Benford's Law, a variety of different data sets include numbers with leading (first)7)____________
digits that follow the distribution shown in the table below. Test for goodness-of-fit with
Benford's Law. $\begin{array}{|l|c|c|c|c|c|c|c|c|c|}\hline \text { Leading Digit } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \begin{array}{l}\text { Benford's law: } \\\text { distribution of } \\\text { leading digits }\end{array} & 30.1 \% & 17.6 \% & 12.5 \% & 9.7 \% & 7.9 \% & 6.7 \% & 5.8 \% & 5.1 \% & 4.6 \% \\\hline\end{array}$
When working for the Brooklyn District Attorney, investigator Robert Burton analyzed the
leading digits of the amounts from 784 checks issued by seven suspect companies. The
frequencies were found to be 0, 18, 0, 79, 476, 180, 8, 23, and 0, and those digits correspond to
the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies
are substantially different from the frequencies expected with Benford's Law, the check
amounts appear to result from fraud. Use a 0.05 significance level to test for
goodness-of-fit with Benford's Law. Does it appear that the checks are the result of fraud?

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Definitions:

Revenue Variances

The difference between actual revenue and budgeted or expected revenue, analyzed to understand and manage financial performance.

Spending Variances

Spending variances are the differences between the actual amount spent and the budgeted or planned amount, often analyzed to control and manage expenses better.

Activity Variance

The difference between the budgeted cost for an activity level and the actual cost incurred, indicating deviations from planned performance.

Net Operating Income

A company's income after operating expenses have been deducted, but before income taxes and interest expenses are taken into account.