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:

Urine Volume

The total amount of urine expelled from the body in a given period, which can vary based on hydration, health, and other factors.

Digestive

Relating to the process by which food is broken down and absorbed by the body.

Gallbladder

A small organ located beneath the liver, storing and concentrating bile produced by the liver before releasing it into the small intestine to aid in digestion.

Liver

A vital organ that performs detoxification, metabolism, and protein synthesis.