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. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | }
\hline \text { Leading Digit } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline \begin{array} { c }
\text { Benford's law: } \
\text { distribution of } \
\text { leading digits }
\end{array} & 30.1 \% & 17.6 \% & 12.5 \% & 9.7 \% & 7.9 \% & 6.7 \% & 5.8 \% & 5.1 \% & 4.6 \% \
\hline
\end{array}$$ 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, 12, 0, 73, 482, 186, 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. What is The value of the test statistic? Does it appear that the checks are the result of fraud?
A) $\chi ^ { 2 } = 15.507$ It does not appear that the checks are the result of fraud.
B) $\chi ^ { 2 } = 3177.409$ It does appear that the checks are the result of fraud.
C) $\chi ^ { 2 } = 15.507$ It does appear that the checks are the result of fraud.
D) $\chi ^ { 2 } = 3177.409$ It does not appear that the checks are the result of fraud.

Question

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. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Leading Digit } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline \begin{array} { c } 
\text { Benford's law: } \
\text { distribution of } \
\text { leading digits }
\end{array} & 30.1 \% & 17.6 \% & 12.5 \% & 9.7 \% & 7.9 \% & 6.7 \% & 5.8 \% & 5.1 \% & 4.6 \% \
\hline
\end{array}$$ 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, 12, 0, 73, 482, 186, 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. What is The value of the test statistic? Does it appear that the checks are the result of fraud? 
A) $\chi ^ { 2 } = 15.507$ It does not appear that the checks are the result of fraud.
B) $\chi ^ { 2 } = 3177.409$ It does appear that the checks are the result of fraud.
C) $\chi ^ { 2 } = 15.507$ It does appear that the checks are the result of fraud.
D) $\chi ^ { 2 } = 3177.409$ It does not appear that the checks are the result of fraud.

Quizplus · Accepted Answer

The test statistic $\chi^2 = 3177.409$ is very large, indicating a significant difference between the observed and expected frequencies, suggesting that the checks are likely the result of fraud.

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