An investigator analyzed the leading digits from 761 checks issued by seven susp

Question

An investigator analyzed the leading digits from 761 checks issued by seven suspect companies. The frequencies were found to be 3, 15, 1, 62, 337, 304, 8, 15, and 16 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 shown below, 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? Determine the null and alternative hypotheses.

Explanation / Answer

Here null Hypothesis : H0 : the numbers follow benford's law. Checks are not fraud.

Alternative Hypothesis : Ha : the numbers doesn't follow benford's law. Checks are fraud

The observed - expected table

According to benford's law

P(d) = log10 (d+1) - log10 (d)

so here X2 = 3006.16

for dF = 8 and alpha = 0.05

X2cr = 15.507

so here X2 > X2cr so we shall reject the null hypothesis and can conclude that checks appeared are the result of fraud.

D Observed Expected (o-E)^2/E 1 3 229.08 223.12 2 15 134.01 105.68 3 1 95.08 93.09 4 62 73.75 1.87 5 337 60.26 1271.00 6 304 50.95 1256.93 7 8 44.13 29.58 8 15 38.93 14.71 9 16 34.82 10.17 761 761 3006.16

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