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:

Output Increases

A rise in the quantity of goods or services produced by a firm or economy.

Scale of Operations

The size or level at which a company or plant is operating, indicating its capacity to produce goods or services.

Average Cost Curve

A graphical depiction showing the cost per unit of output at different levels of production, reflecting the variability in total cost over volume.

Positive Profit

A financial gain that occurs when the revenues received from business activities exceed the expenses, costs, and taxes needed to sustain the activity.