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 165 checks to a supposed company are as follows: Digit 1 2 3 4 5 6 7 8 9 Observed Frequency 47 27 11 22 14 15 5 15 9 a. State the appropriate null and alternative hypotheses for this test. b. Explain why α=0.01α=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? Reject the Null Hypothesis Fail to 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. I need parts C,D,E answered. Thank you!!
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 165 checks to a supposed company are as follows:
| Digit | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Observed Frequency |
47 | 27 | 11 | 22 | 14 | 15 | 5 | 15 | 9 |
a. State the appropriate null and alternative hypotheses for this test.
b. Explain why α=0.01α=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?
- Reject the Null Hypothesis
- Fail to 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.
I need parts C,D,E answered. Thank you!!
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