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

question 56

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:

Water Table

The level below the Earth's surface at which the ground is saturated with water.

Artesian

Groundwater that is in a confined aquifer and is under enough water pressure to rise above the level of the aquifer.

Water Table

The water table is the upper level of an underground surface in which the soil or rocks are permanently saturated with water, delineating the boundary between the aquifer's unsaturated zone and saturated zone.

Topography

The arrangement of the natural and artificial physical features of an area, including its relief and the position of its features.