According to Benford's Law, a Variety of Different Data SetsWhen Working for the Brooklyn District Attorney, Investigator Robert Burton

The Answer is Test statistic χ 2 = 3590.094 \chi ^ { 2 } = 3590.094 χ 2 = 3590.094 . Critical value: χ 2 = 15.507. P \chi ^ { 2 } = 15.507 . P χ 2 = 15.507. P -value < 0.005 < 0.005 < 0.005 . There is sufficient evidence to warrant rejection of the claim that the leading digits are from a population with a distribution that conforms to Benford's Law. It does appear that the checks are the result of fraud.

According to Benford's Law, a Variety of Different Data SetsWhen Working for the Brooklyn District Attorney, Investigator Robert Burton

The Answer is Test statistic χ 2 = 3590.094 \chi ^ { 2 } = 3590.094 χ 2 = 3590.094 . Critical value: χ 2 = 15.507. P \chi ^ { 2 } = 15.507 . P χ 2 = 15.507. P -value < 0.005 < 0.005 < 0.005 . There is sufficient evidence to warrant rejection of the claim that the leading digits are from a population with a distribution that conforms to Benford's Law. It does appear that the checks are the result of fraud.

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

question 2

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?

Definitions:

Bounded Rationality

A concept in decision-making that suggests individuals are limited in their ability to process information, leading to satisficing rather than optimal decisions.

Groupthink

A phenomenon in decision-making where the desire for consensus within a group can lead to poor choices and suppress dissenting viewpoints.

Divergent Thinking

A mental strategy or procedure aimed at fostering innovative ideas by investigating a wide range of possible options.

Verification Stage

A phase in various processes where the validity or accuracy of something is checked or confirmed, often used in the context of testing or quality assurance.