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

question 23

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:

Constrained Resource

A factor that limits the output of a process or system, such as a machine, worker, or material that is in short supply.

Contribution Margin

The amount remaining from sales revenue after variable expenses are deducted, indicating how much contributes to covering fixed costs and profit.

Special Order

An order for goods or services that is outside the company's normal production routine or product range.

Resale Value

The estimated amount that an asset or good will be sold for at the end of its useful life.