Question

The IRS currently uses Benford's Law to detect fraudulent tax data. Suppose you work for the IRS and are investigating an individual suspected of embezzling. The first digit of 162 checks to a supposed company are as follows:

Digit	1	2	3	4	5	6	7	8	9
Observed Frequency	46	32	20	21	13	12	6	2	10

What is the P-Value? Report answer to 4 decimal places
P-Value =

Write a statement to the law enforcement officials that will use it to decide whether to pursue the case further or not. Structure your essay as follows:

Given a brief explanation of what a Goodness of Fit test is.
Explain why a Goodness of Fit test should be applied in this situation.
State the hypotheses for this situation.
Interpret the p-value
Use the answer to part c to justify the decision in part d.
Use the decision in part d to make a conclusion about whether the individual is likely to have embezzled.
Use this to then tell the law enforcement officials whether they should pursue the case or not.

Answer 1

category	observed frequencey, O	expected proportion	expected frequency,E	(O-E)	(O-E)/√E	(O-E)²/E
1	46	0.111	18.00	28.00	6.600	43.556
2	32	0.111	18.00	14.00	3.300	10.889
3	20	0.111	18.00	2.00	0.471	0.222
4	21	0.111	18.00	3.00	9.00	0.500
5	13	0.111	18.00	-5.00	25.00	1.389
6	12	0.111	18.000	-6.00	36.00	2.000
7	6	0.111	18.000	-12.00	144.00	8.000
8	2	0.111	18.000	-16.00	256.00	14.222
9	10	0.111	18.000	-8.00	64.00	3.556

Ho: distribution follow Benford's Law

Ha: distribution does not follow Benford's Law

chi square test statistic,X² = Σ(O-E)²/E =   84.333              
                  
level of significance, α=   0.01              
Degree of freedom=k-1=   9   -   1   =   8
                  
P value =   0.0000   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho