Question

The first signifcant digit in any number must be 1.2. 3. 4. 5.0.7.8. or e. It was discovered that Srst 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 exampe te o own g der but on represents the frst digits n 220 al eged y fraudulent check wrtten to ฮ bogus oompany by an employee attempting to embezze unds om his employer. Complete parts 3 through c) below Fi Distribution of first digits (Benford's Law) igit obability 0.301 0.176 0.125 0.097 0.079 Probability 0.067 0.058 0.051 0.046 First digits in allegedly fraudulent checks First digit Frequency 42 32 28 20 36 15 (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 α= (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 altemative hypotheses? OA. The distribution of the first digits in the allegedly fraudulent checks does not obey Benford's Law O B. 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 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? | (Round to three decimal places as needed.) χ What is the range of P-values for the test? The range of P-values for the test is Using the P value approach, compare the range of P values with the g en α-001 level of significance Based on the results do the first digits obey Benf 's Law? Do not reject the Ho because the range of P-values is less than the given α level of significance. A. Do not reject the Ho because the range of P-values is greater than the given α level of significance B. C. O Reject the Ho because the range of P-values is less than the given o level of significance O D. Reject the Ho because the range of P-values 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? O A. Yes, the first digits do not obey Benford's Law O B. Yes, the first digits obey Benford's Law O C. No, the d the first digits do not obey Benford's Law No, the first digits obey Benford's Law. D.

Answer 1

a)alpha =0.01

b) option B is correct for hypothesis:

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	42	66.22	-2.98	8.858
2	0.176	32	38.72	-1.08	1.166
3	0.125	28	27.50	0.10	0.009
4	0.097	20	21.34	-0.29	0.084
5	0.079	24	17.38	1.59	2.522
6	0.067	36	14.74	5.54	30.664
7	0.058	15	12.76	0.63	0.393
8	0.051	16	11.22	1.43	2.036
9	0.046	7	10.12	-0.98	0.962
total	1.000	220	220		46.695

X² =46.695

the range of p values <0.0001

option C is correct :Reject HO ;..is less than

c)

option A is correct