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

question 72

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:

Win-Lose Conflict

A type of conflict resolution in which one party's gain is another party's loss, emphasizing competition over collaboration.

Competing

Engaging in a struggle or contest against others for resources, recognition, or victory in a specific area.

Compromising

The act of finding a middle ground through mutual concessions in a dispute or negotiation.

Personalities

Personalities encompass the unique combination of emotional, attitudinal, and behavioral response patterns of an individual, contributing to their consistent behaviors and actions in various situations.