Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digitdisproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, theprobability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very largecorporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 227numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in thecomputer 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 > 0.301O Ho: P> 0.301; H₁: p = 0.301O Ho: P= 0.301; H₁: p = 0.301O 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.-2-202244-2-20022(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statisticallysignificant 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 therevenue 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 inthe 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 thatthe books have been "cooked" by artificially lowering numbers in the file? Comment from the point of view of the InternalRevenue Service. Comment from the perspective of the Federal Bureau of Investigation as it looks for "profit skimming" byunscrupulous 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 befalse. We can say that the probability is a that we made a mistake in rejecting H. Based on the outcome of the test, would yourecommend 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 notmerited.

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.)

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.

Chapter1: Functions

Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy

Problem 7EA

See similar textbooks