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

question 91

Essay

According to Benford's Law, a variety of different data sets include numbers with leading (first) 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:

Documents of Title

Legal documents that provide proof of ownership of property, including titles for vehicles or deeds for real estate.

Warehouse Receipts

Documents issued by warehouse operators certifying the possession and storage of specified goods.

Bills of Lading

Official documents issued by a carrier to acknowledge the receipt of cargo for shipment.

Accession

A method of acquiring property rights by adding value to personal property through labor or new materials.