Question

An investigator analyzed the leading digits from 799 checks issued by seven suspect companies. The frequencies were found to be 3, 18, 3, 87, 322, 328, 8, 20, and 10, 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 0.10 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the resuit of fraud? Leading Digit Actual Frequency Benford's Law: Distribution of Leading Digits 8 4 3 3 12.5% 5 322 7.9 % 2 18 10 20 328 6.7% 87 4.6 % 5.8 % 5.1% 9.7% 30.1% 17.6%

Answer 1

Null hypothesis: In Chi-Square goodness of fit test, the null hypothesis assumes that there is no significant difference between the observed and the expected value.

Alternative hypothesis: In Chi-Square goodness of fit test, the alternative hypothesis assumes that there is a significant difference between the observed and the expected value.

Fon this problem goodness of fit chi-squene test of is the appropiate one Test statistic , x = { observed - Expected) Expected = = 3(x - Ne: * where N = Total no. of observations T : 799 here pi ith percentage so X = (3 - 799 x 0.301) + (18 – 799 70.676) 799x0.30 799x0.176 +---- + (10 – 799 x 0.046). 79900.046 = X = 2967.3 The best startnike follows chi-squene distribution with of n-1 = 9-1= 8

Decision rule: Reject the null hypo. | Т4 т.р. м x x x - Fon, d = o.1 and n=9. Want = 2.733_, 15.507 So, X = 2967. 3 Z Xan then we conclude the observed freq are substanbakially different which mean the checks are the result of hand NOVEMBER