Extra Credit: Earn 5 points extra credit if all answers are correct. 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. Table of data Leading Digit 1 2 3 4 5 6 7 8 9 Distribution of Benford’s Law 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% 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 as shown in the table below. Table of data Leading Digit 1 2 3 4 5 6 7 8 9 Frequency 0 9 0 70 485 189 8 23 0 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? What is the test statistic? [test] (round to 2 decimal places) What is the p-value? [pvalue] (round to 4 decimal places) Does it appear the checks are the result of fraud? [fraud] (type yes or no)
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