Question

An investigator analyzed the leading digits from 784 checks issued by seven suspect companies. The frequencies were found to be 248, 150, 99, 57, 74, 61, 46, 39, 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 0.025 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud? 

Answer 1

The statistical software output for this problem is:

Chi-Square goodness-of-fit results:

Observed: Oi
Expected: Ei

N	DF	Chi-Square	P-value
784	8	29.022896	0.0003

Hence,

Ho: The leading digits are from the population that confirms to Benford's law.

H1: Atleast one leading digits has a frequency that does not confirm to Benford's law.

Test statistic = 29.023

P-value = 0.0003

Reject; is