According
Digits That Follow the Distribution Shown in the Table

question 50

Essay

According
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:

UCC

The Uniform Commercial Code, a comprehensive set of laws governing commercial transactions in the United States, aimed at harmonizing the law of sales and other commercial transactions.

Common Law

A legal system characterized by judicial decisions based on customs and prior judicial judgments, rather than by written statutes or codes.

Risk Of Loss

Refers to the legal responsibility for damages or losses of goods, especially in transactions or during shipment, indicating who bears the financial burden.

Future Goods

Futures goods are items that are to be manufactured, produced, or acquired by the seller after the sale has been made.