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:

Mutual Ownership

Refers to an arrangement where entities are owned by their members who share profits or benefits.

Consolidated Balance Sheet

A financial statement that shows the financial position of a parent company and its subsidiaries as if they were a single entity.

Treasury Stock Approach

A method in finance that accounts for repurchased shares of a company's own stock as treasury stock, reducing the total equity in the balance sheet.

Attributed Ownership

The assignment of ownership interest in a company or property, often for the purpose of determining control or tax responsibilities.