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.

The probability of getting a number with "1" as the leading digit is about 0.301.Sample size Number…

Answered: Recall that ims that very large data…

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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The best way to ensure that your sample represents the population it came from accurately, is to make sure you have a sample of at least 10. (n=10) True or false
Does it seem to you that people tend to be absent more on some days of the week than on others? Recently, a major biotechnology firm collected data with the hope of determining whether or not its employees were more likely to be absent on some weekdays than on others. The firm examined a random sample of 110 employee absences. The distribution of these 110 absences is shown in the table below. The observed frequency for each category (each weekday) is shown in the first row of numbers. The second row of numbers contains the frequencies expected for a sample of 110 employees if employee absences at the firm are equally likely on each of the five weekdays. The bottom row of numbers contains the following value for each of the categories. (fo-fE) (Observedrequency Expectedrequency JE Part 1 Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. 2 Round your responses to three or more decimal places. (SO-SE)² SE Send data…
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Use the following scenario to answer the next 6 questions: M&Ms are your favorite vending machine snack and you purchase them often. Lately, it seems like the bags have been having a disproportionate distribution of the colors. The company claims that 24% of the candies per bag should be blue. You decide to test this claim for yourself. You purchase a large bag and find that 38 of the 224 candies are blue. Before complaining to the company, you want to be fairly sure of your accusation, so you set a 1% significance level for your test. Do you have sufficient evidence that the color distribution is different than advertised? Based on the data, the value of the test statistic is:
If two large random samples are drawn from two populations, each having a mean of $100, the relevant sampling distribution of their difference has a mean of a. 200 b. The Sum of the 2 Sample Means C. 0 D. The difference between the two sample means.

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