Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 225 numerical entries from the file and r = 51 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.(i) Test the claim that p is less than 0.301. Use ? = 0.05. Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. Infact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit isabout 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let ussay you took a random sample of n = 225 numerical entries from the file and r = 51 of the entries had a first nonzero digit of 1. Let p represent thepopulation proportion of all numbers in the corporate file that have a first nonzero digit of 1. (ii) If p is in fact less than 0.301, would it make you suspect that there are not enough numbers in the data file with leading 1's? Could this indicate that the books have been "cooked" by "pumping up" or inflating the numbers? Comment from the viewpoint of astockholder. Comment from the perspective of the Federal Bureau of Investigation as it looks for money laundering in the form of false profits.O Yes. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.O No. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts.O No. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.O Yes. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts.(iii) Comment on the following statement: If we reject the null hypothesis at level of significance a, we have not proved H. to be false. We can say that the probability is a that we made a mistake in rejecting Hạ. Based on the outcome of the test, would yourecommend further investigation before accusing the company of fraud?O we have not proved Ho to be false. Because our data lead us to accept the null hypothesis, more investigation is not merited.O we have not proved Ho to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.O we have proved H, to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.O we have not proved Ho to be false. Because our data lead us to reject the null hypothesis, more investigation is merited.

The following information is provided: The sample size is N=225N = 225, the number of entries had a…

Answered: Recall that Benford's Law claims that…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 27E: Another friend asks you to explain how to tell whether two events are dependent or independent. How...

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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 225 numerical entries from the file and r = 51 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.

(i) Test the claim that p is less than 0.301. Use ? = 0.05.

(ii) If p is in fact less than 0.301, would it make you suspect that there are not enough numbers in the data file with leading 1's? Could this indicate that the books have been "cooked" by "pumping up" or inflating the numbers? Comment from the viewpoint of a
stockholder. Comment from the perspective of the Federal Bureau of Investigation as it looks for money laundering in the form of false profits.
O Yes. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.
O No. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts.
O No. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.
O Yes. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts.
(iii) Comment on the following statement: If we reject the null hypothesis at level of significance a, we have not proved H. to be false. We can say that the probability is a that we made a mistake in rejecting Hạ. Based on the outcome of the test, would you
recommend further investigation before accusing the company of fraud?
O we have not proved Ho to be false. Because our data lead us to accept the null hypothesis, more investigation is not merited.
O we have not proved Ho to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.
O we have proved H, to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.
O we have not proved Ho to be false. Because our data lead us to reject the null hypothesis, more investigation is merited.

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