Recall that ims that very large data 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 bank. You draw a random sample of n = 227 numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. (i) Test the claim that p is more than 0.301. Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. OHO: P= 0.301; H₁: p > 0.301 OHO: p > 0.301; H₁: p = 0.301 OH: P = 0.301; H₂: p = 0.301 O Ho: P= 0.301; H₂: p < 0.301 (b) What sampling distribution will you use? O The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq > 5. O The standard normal, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.)
Recall that ims that very large data 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 bank. You draw a random sample of n = 227 numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. (i) Test the claim that p is more than 0.301. Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. OHO: P= 0.301; H₁: p > 0.301 OHO: p > 0.301; H₁: p = 0.301 OH: P = 0.301; H₂: p = 0.301 O Ho: P= 0.301; H₂: p < 0.301 (b) What sampling distribution will you use? O The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq > 5. O The standard normal, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.)
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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Transcribed Image Text: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 bank. You draw a random sample of n = 227
numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the
computer file that have a leading digit of 1.
(i) Test the claim that p is more than 0.301. Use α = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
Ho: P = 0.301; H₁: p > 0.301
O Ho: P> 0.301; H₁: p = 0.301
O Ho: P= 0.301; H₁: p = 0.301
O Ho: p = 0.301; H₂: p < 0.301
(b) What sampling distribution will you use?
The standard normal, since np < 5 and nq < 5.
The Student's t, since np < 5 and nq < 5.
The Student's t, since np > 5 and nq > 5.
The standard normal, since np > 5 and nq > 5.
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.)
Sketch the sampling distribution and show the area corresponding to the P-value.
-2
-2
0
2
2
4
4
-2
-2
0
0
2
2
(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 a?
O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the x = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
O There is sufficient evidence at the 0.05 level to conclude that the true proportion of numbers with a leading 1 in the
revenue file is greater than 0.301.
There is insufficient evidence at the 0.05 level to conclude that the true proportion of numbers with a leading 1 in
the revenue file is greater than 0.301.
(ii) If p is in fact larger than 0.301, it would seem there are too many numbers in the file with leading 1's. Could this indicate that
the books have been "cooked" by artificially lowering numbers in the file? Comment from the point of view of the Internal
Revenue Service. Comment from the perspective of the Federal Bureau of Investigation as it looks for "profit skimming" by
unscrupulous employees.
No. There seems to be too many entries with a leading digit 1.
Yes. There does not seem to be too many entries with a leading digit 1.
O Yes. There seems to be too many entries with a leading digit 1.
O No. There does not seem to be too many entries with a leading digit 1.
(iii) Comment on the following statement: If we reject the null hypothesis at level of significance &, we have not proved Ho to be
false. We can say that the probability is a that we made a mistake in rejecting H. Based on the outcome of the test, would you
recommend further investigation before accusing the company of fraud?
We have not proved Ho to be false. Because our data lead us to reject the null hypothesis, more investigation is merited.
We have not proved Ho to be false. Because our data lead us to reject the null hypothesis, more investigation is not
merited.
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