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:

Equilibrium Wage

The wage rate at which the quantity of labor supplied equals the quantity of labor demanded.

Labor Demand Curve

A graphical representation showing the relationship between the wage rate and the quantity of labor that employers are willing to hire.

Purely Competitive Seller

A seller operating in a market where goods are homogeneous, and there are no barriers to entry, allowing for many competitors.

Derived Demand

Demand for a factor of production or intermediate good that occurs as a result of the demand for another related final good or service.