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. The first digit of 146 checks to a supposed company are as follows: Digit 1 2 34 56 |7|8 |9 Observed Frequency 36 23 12 20 17 107| 147 a. State the appropriate null and alternative hypotheses for this test. b. Explain why a = 0.01 is an appropriate choice for the level of significance in this situation. c. What is the P-Value? Report answer to 4 decimal places P-Value = d. What is your decision? O Fail to reject the Null Hypothesis O Reject the Null Hypothesis
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. The first digit of 146 checks to a supposed company are as follows: Digit 1 2 34 56 |7|8 |9 Observed Frequency 36 23 12 20 17 107| 147 a. State the appropriate null and alternative hypotheses for this test. b. Explain why a = 0.01 is an appropriate choice for the level of significance in this situation. c. What is the P-Value? Report answer to 4 decimal places P-Value = d. What is your decision? O Fail to reject the Null Hypothesis O Reject the Null Hypothesis
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text: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. The first digit of 146 checks to a
supposed company are as follows:
Digit
1
2
3
4
5
6 78
Observed
36 23 | 12 20 | 17 107 14 7
Frequency
a. State the appropriate null and alternative hypotheses for this test.
b. Explain why a = 0.01 is an appropriate choice for the level of significance in this situation.
c. What is the P-Value? Report answer to 4 decimal places
P-Value =
d. What is your decision?
O Fail to reject the Null Hypothesis
O Reject the Null Hypothesis
e. 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 answer to part c.
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.
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