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:

Short-Term Investment

A short-term investment is an asset that is expected to be converted into cash or sold within a short period, typically one year, to generate income.

Unrealized Gains and Losses

Profits or losses that arise from changes in the value of investments or assets that have not yet been sold or realized.

Other Comprehensive Income

A component of shareholders' equity, consisting of income that is not realized and hence not included in the net income (loss), such as unrealized gains or losses on available-for-sale securities.

GAAP

Generally Accepted Accounting Principles, which are a set of rules and standards for financial reporting used in the United States.