Question

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 194 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Complete parts (a) through (c) below. Click the icon to view the tables (a) Because these data are meant to prove that someone is guilty of fraud, what would be an appropriate level of significance when performing a goodness-of-fit test? Use - (b) Using the level of significance chosen in part (a), test whether the first digits in the allegedly fraudulent checks obey Benford's Law. Do the first digits obey Benford's Law? What are the null and alternative hypotheses? O A. Ho: The distribution of the first digits in the allegedly fraudulent checks does not obey Benford's Law. H: The distribution of the first digits in the allegedly fraudulent checks obeys Benford's Law. OB. Ho: The distribution of the first digits in the allegedly fraudulent checks obeys Benford's Law. H,: The distribution of the first digits in the allegedly fraudulent checks does not obey Benford's Law. What is the test statistic? x =(Round to three decimal places as needed.) What is the P-value of the test? P-value - (Round to three decimal places as needed.) Using the P-value approach, compare the P-value with the given a = 0.01 level of significance. Based on the results, do the first digits obey Benford's Law? A. Do not reject the H, because the calculated P-value is less than the given a level of significance. OB. Reject the H, because the calculated P-value is less than the given a level of significance. c. Reject the H, because the calculated P-value is greater than the given t level of significance. OD. Do not reject the H, because the calculated P-value is greater than the given a level of significance. (c) Based on the results of part (b), could one think that the employee is guilty of embezzlement? A. No, the first digits do not obey Benford's Law. OB. No, the first digits obey Benford's Law. OC. Yes, the first digits obey Benford's Law. OD. Yes, the first digits do not obey Benford's Law.

Answer 1

a) α =0.10

b)

OB. He: The distribution of the first digits in the allegedly fraudulent checks obeys Benford's Law. H,: The distribution of the first digits in the allegedly fraudulent checks does not obey Benford's Law.

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
Category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.301	36	58.39	-2.931	8.588
2	0.176	25	34.14	-1.565	2.449
3	0.125	28	24.25	0.762	0.580
4	0.097	26	18.82	1.656	2.741
5	0.079	23	15.33	1.960	3.843
6	0.067	17	13.00	1.110	1.232
7	0.058	15	11.25	1.117	1.248
8	0.051	17	9.89	2.259	5.104
9	0.046	7	8.92	-0.644	0.415
total	1.00	194	194	3.724381673	26.20
test statistic X02 =		26.199

p value =

0.001

from excel: chidist(26.199,8)

OB. Reject the H, because the calculated P-value is less than the given a level of significance.

c_)

OD. Yes, the first digits do not obey Benford's Law.