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 = 217
numerical entries from the file and r = 52 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
α = 0.05.
What is the value of the sample test statistic? (Round your answer
to two decimal places.)
(c) Find the P-value of the test statistic. (Round your
answer to four decimal places.)
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(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.
Yes. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.
No. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.
No. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts.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 α, we have not proved
Ho to be false. We can say that the probability
is α that we made a mistake in rejecting Ho.
Based on the outcome of the test, would you recommend further
investigation before accusing the company of fraud?
We have not proved H0 to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.
We have not proved H0 to be false. Because our data lead us to accept the null hypothesis, more investigation is not merited.
We have proved H0 to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.
We have not proved H0 to be false. Because our data lead us to reject the null hypothesis, more investigation is merited.
i)test statistic =-1.97 ( please try -1.96 if this comes wrong and revert)
p value =0.0244 please try 0.0250 if this comes wrong and revert)
At the α = 0.05 level, we reject the null hypothesis and
conclude the data are statistically significant.
Yes. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.
We have not proved H0 to be false. Because our data lead us to reject the null hypothesis, more investigation is merited.
Recall that Benford's Law claims that numbers chosen from very large data files tend to have...
1.) 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...
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....
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 the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data...
Benford's Law claims that numbers chosen from very large data files tend to have "l" 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 "l" as the leading digit is about 0.301. 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...
Benfords 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. 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...
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. 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...
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 "I" as the leading digit is about 0.301. 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...
20.) 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. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us...
Points out ofs.eo Not yet answered P Flag question 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. Suppose you are an auditor for a very large corporation. The revenue report involves millions of...
Question Part Points Submissions Used 1.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...