You might think that if you looked at the first digit in randomly selected numbers that the distribution would be uniform. Actually, it is not! Simon Newcomb, and later Frank Benford, both discovered that the digits occur according to the following distribution. Digit Probability 1 0.301 2 0.176 3 0.125 4 0.097 5 0.079 6 0.067 7 0.058 8 0.051 9 0.046 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. If the leading digit for the suspect is different from the proportions in the above table, then the individual may be guilty of embezzling. Use Alpha=0.01. The first digit of 152 checks to a supposed company are as follows: Digit Observed Frequency 1 40 2 31 3 21 4 17 5 5 6 5 7 13 8 13 9 7 a. Choose the appropriate null hypothesis for this test. H0: At least one proportion is different. H0: p1≠p2≠p3≠p4≠p5≠p6≠p7≠p8≠p9 H0:p1=0.301,p2=0.176,p3=0.125,p4=0.097,p5=0.079,p6=0.067,p7=0.058,p8=0.051,p9=0.046 H0: p1=p2=p3=p4 H0: The individual has been caught embezzling. b. What is the value of the test statistic. Round answer to at least 4 decimal places. What is the P-Value? Round answer to at least 4 decimal places. P-Value = c. What is your decision? Fail to reject the Null Hypothesis Reject the Null Hypothesis Use the decision in part d to make a conclusion about whether the individual is likely to have embezzled. There is no evidence that the individual is embezzling. The evidence shows that the individual may be guilty of embezzling.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

You might think that if you looked at the first digit in randomly selected numbers that the distribution would be uniform. Actually, it is not! Simon Newcomb, and later Frank Benford, both discovered that the digits occur according to the following distribution.

Digit	Probability
1	0.301
2	0.176
3	0.125
4	0.097
5	0.079
6	0.067
7	0.058
8	0.051
9	0.046

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. If the leading digit for the suspect is different from the proportions in the above table, then the individual may be guilty of embezzling. Use Alpha=0.01. The first digit of 152 checks to a supposed company are as follows:

Digit	Observed Frequency
1	40
2	31
3	21
4	17
5	5
6	5
7	13
8	13
9	7

a. Choose the appropriate null hypothesis for this test.

H0: At least one proportion is different.
H0: p1≠p2≠p3≠p4≠p5≠p6≠p7≠p8≠p9
H0:p1=0.301,p2=0.176,p3=0.125,p4=0.097,p5=0.079,p6=0.067,p7=0.058,p8=0.051,p9=0.046
H0: p1=p2=p3=p4
H0: The individual has been caught embezzling.

b. What is the value of the test statistic. Round answer to at least 4 decimal places.

What is the P-Value? Round answer to at least 4 decimal places.
P-Value =

c. What is your decision?