Question

An investigator analyzed the leading digits from

796796

checks issued by seven suspect companies. The frequencies were found to be

55​,

1818​,

00​,

8989​,

224224​,

412412​,

88​,

1717​,

and

2323​,

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

0.0250.025

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	55	1818	00	8989	224224	412412	88	1717	2323
​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%

Determine the null and alternative hypotheses.

Upper H 0H0​:

The leading digits are from a population that conforms to Benford's law.

Upper H 1H1​:

At least one leading digit has a frequency that does not conform to Benford's law.

Calculate the test​ statistic,

chi squaredχ2.

chi squaredχ2equals=nothing

​(Round to three decimal places as​ needed.)

Enter your answer in the answer box and then click Check Answer.

Answer 1

(a)

H0: The leading digits are from a population that conforms to Benford's law

H1: At least one leading digit ha afrequency that does not conform to Benford;s law.

(b)

The statistic is calculated as follows:

Leading Digit	Observed Frequency (O)	Expected Frequency (E)	(O - E)2/E
1	5	796X30.1/100=239.596	229.700
2	18	796X17.6/100=140.096	106.409
3	0	796X12.5/100=99.5	99.500
4	89	796X9.7/100=77.212	1.7997
5	224	796X7.9/100=62.884	412.798
6	412	796X6.7/100=53.332	2412.116
7	8	796X5.8/100=46.168	31.554
8	17	796X5.1/100=40.596	13.715
9	23	796X4.6/100=36.616	5.063
Total = =			3312.685

= 3312.685