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reject/do not reject is/is not does appear/ does not appear An investigator anal

ID: 3323793 • Letter: R

Question

reject/do not reject is/is not does appear/ does not appear

An investigator analyzed the leading digits from 786 cherks isued by seven suspect companies The frequencies were found to be 1, 12, 5,69, 206, 446,5, 17, and 25, and thase digits comespond to the leading digits of 1,2, 3, 4,5,6,7, 8, and 9, respectively If the observad frequencies are substantially different from the frequencies expected with Benford's law shown balow, tha check amounts appear to result from fraud. Us a 0.01 significance laval to tes for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud? Leading Digit Benfords Law: Distribution of Leading Digits Determine the null and alternative hypotheses Ho H1: Calculate the test statstic, x x2 (Round to three decimal places as needed.) Calculats the P-value P-value-L Round to four decimal places as needed.) State the conclusion 9% 6% At most three leading digits have frequencies that do not conform to Benford's law. At least ane leading digit has a frequency that doas not conform to Benford's law At least two leading digits have frequencies that do not conform to Benfords law. The leading diglts are from a populatlon that conforms to Benford's law H0 There clant cvidence to warrant re action o he darn that the lnading digits are from a population with a distribution that conforms to Ben ar s law It su that the checks are the result of fraud En

Explanation / Answer

Below are the null and alternate hypothesis

H0: probabilities are as per distribution law

H1: probabilities are not as per distribution law

chi-square = 3763.43

df = 8

p-value = 0.0000

Reject H0. There are sufficient evidence.

It concludes that there is case of fraud

Leading Digits Observed F (Oi) as per Law Expected F(Fi) (Oi - Ei)^2/Ei 1 1 30.10% 236.586 234.5902268 2 12 17.60% 138.336 115.3769438 3 5 12.50% 98.25 88.50445293 4 69 9.70% 76.242 0.687895963 5 206 7.90% 62.094 333.5094669 6 446 6.70% 52.662 2937.882766 7 5 5.80% 45.588 36.13638993 8 17 5.10% 40.086 13.29549958 9 25 4.60% 36.156 3.442204226 Total 786 3763.425846