Question

An investigator analyzed the leading digits from

792

checks issued by seven suspect companies. The frequencies were found to be 44​,13,55​,71,483,175,55​,19 and 17​,

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?

Leading Digit	1	2	3	4	5	6	7	8	9
Actual Frequency	44	13	55	71	483	175	55	19	17
​Benford's Law: Distribution of Leading Digits	​30.1%	​17.6%	​12.5%	​9.7%	​7.9%	​6.7%	​5.8%	​5.1%	​4.6%

Calculate the test​ statistic,chi squaredχ2.

Answer 1

(Note : here total number of checks issued are 932 while above given is 792 ; please revert)

Applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.301	44	280.53	-14.12	199.433
2	0.176	13	164.03	-11.79	139.062
3	0.125	55	116.50	-5.70	32.466
4	0.097	71	90.40	-2.04	4.165
5	0.079	483	73.63	47.71	2276.110
6	0.067	175	62.44	14.24	202.883
7	0.058	55	54.06	0.13	0.016
8	0.051	19	47.53	-4.14	17.127
9	0.046	17	42.87	-3.95	15.613
total	1.000	932	932		2886.876

test​ statistic,chi squaredχ2 =2886.876

( please revert if there are other parts of this)