JWitte_Module06_WeeklyAssignment_111116.docx

# JWitte_Module06_WeeklyAssignment_111116.docx - Name_Jordan...

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Name:__Jordan Witte____________________________________ Module 6 Homework Assignment An investigator analyzed the leading digits of the amounts from 200 checks issued by three suspect companies. The frequencies were found to be 68, 40, 18, 19, 8, 20, 6, 9, 12 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 be the result of fraud. Use a 0.05 significance level to test for goodness-of-fit with Benford's law. 1. Calculate the χ 2 test statistic. Solution: In order to find our solution, we should graph out our findings: Digit 1 2 3 4 5 6 7 8 9 Observed 68 40 18 19 20 6 9 12 8 Expected 60 35 25 19 16 13 12 10 9 Benford’s Law 30.1 % 17.6% 12.5% 9.7% 7.9% 6.7 % 5.8% 5.1% 4.6% Leading Digits Probability First Digit Observed Expected 200*prob. (O-E)²/E 0 0.1197 1 0.3010 68 60 1.011 2 0.1761 40 35 0.649 3 0.1249 18 25 1.950 4 0.0969 19 19 0.007 5 0.0792 8 16 3.880 6 0.0669 20 13 3.275 7 0.0580 6 12 2.703 8 0.0512 9 10 0.490 9 0.0458 12 9 0.881 TOTAL 14.847 χ 2 = 14.847 Instructor Comments: 2. Calculate the χ 2 critical value.

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