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Benford's Law and Critical Thinking

When testing for goodness-of-fit with Benford's law, it is necessary to combine categories because not all expected values are at least 5. I don't understand this , use one category with leading digits of 1 , a second category with leading digits of 2,3,4 5 and a third category with leading digits of 6,7,8,9.Are the expected values for these three categories all at least 5? Is there sufficient evidence to conclude that the leading digits on the checks do not conform to Benford's law? Apart from the leading digits, is there any other patterns suggesting that the check amounts were created by the defendant instead of being the result of typical and real transactions? Based on the evidence, if you were a juror, would you conclude that the check amounts are the result of fraud? What could be one argument if I was the attorney for the defendant?

THESE ARE THE AMOUNTS OF THE CHECKS.
these checks are in order by row.

$1,927.48 $27,902.31 $86,241.90 $72,117.46 $81,321.75 $97,473.96
$93,249.11 $89,658.16 $87,776.89 $92,105.83 $79,949.16 $87,602.93
$96,879.27 $91,806.47 $84,991.67 $90,831.83 $93,766.67 $88,336.72
$94,639.49 $83,709.26 $96,412.21 $88,432.86 $71,552.16

Solution Summary

Step by step solution of testing for goodness-of-fit with Benford's law.

$2.19