According Digits That Follow the Distribution Shown in the Table

question 30

Multiple Choice

According 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 $0,12,0,73,482,186,8,23$ , 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 frequenciesare 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) \(\chi ^ { 2 } = 3711.409\) It does appear that the checks are the result of fraud.
• B) \(\chi ^ { 2 } = 3711.409\) It does not 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) \(\chi ^ { 2 } = 15.507\) It does not appear that the checks are the result of fraud.

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