Explanation Given Information: The distribution of first digits of Good neighbor, Inc.’s tax returns is: y 1 2 3 4 5 6 7 8 9 P ( Y = y ) 0.31 0.16 0.13 0.11 0.07 0.07 0.05 0.06 0.04 The sample size is n = 1000 . Consider the distribution of first digits of Good neighbor, Inc.’s tax returns: y 1 2 3 4 5 6 7 8 9 P ( Y = y ) 0.31 0.16 0.13 0.11 0.07 0.07 0.05 0.06 0.04 To compute the 95 % certainty compare the sum of squares of error (SSE) to the largest error that would have been expected to get by chance in 95 out of 100 selections of data. The biggest error is computed using the “chi-square” distribution. If the SSE is less than the chi-square value then 95 % certainty is not obtained. Compute the chi-squared value using MS-Excel by entering, " = CHISQ .INV .RT ( 0.05 , 8 ) " . Where 0.05 is 1 − 0 .95 denoting the 95 % certainty and 8 is the degrees of freedom = number of outcomes − 1 . Compute the SSE to determine how far a data value deviates from the value according to the Benford’s law using the formula, S S E = n [ P ( y 1 ) − P ( x 1 ) P ( x 1 ) + P ( y 2 ) − P ( x 2 ) P ( x 2 ) + ... + P ( y 9 ) − P ( x 9 ) P ( x 9 ) ] Where P ( y i ) are the probabilities in the Good are neighbor, Inc

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 8, Problem 7CS

To determine

Whether the following distribution of first digits of Good neighbor, Inc.’s tax returns with a sample size of n=1000 fails, with 95% certainty, to follow Benford’s law:

y 1 2 3 4 5 6 7 8 9

P(Y=y) 0.31 0.16 0.13 0.11 0.07 0.07 0.05 0.06 0.04

Expert Solution & Answer

Chapter 8 Solutions

Finite Mathematics

Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - In Exercises 110, classify the random variable X...

Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - Prob. 13E Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - The random variable X has the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - Prob. 23E Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - 2010 Income Distribution up to $100,000 The...Ch. 8.1 - 2003 Income Distribution up to $100,000 Repeat...Ch. 8.1 - Population Age in Mexico The following chart shows...Ch. 8.1 - Population Age in the United States Repeat...Ch. 8.1 - Sport Utility VehiclesTow Ratings The following...Ch. 8.1 - Housing Prices Going into the Real Estate Bubble...Ch. 8.1 - Stock Market Gyrations The following chart shows...Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Test Scores Your scores for the 20 surprise math...Ch. 8.1 - Car Purchases To persuade his parents to...Ch. 8.1 - Car Purchases Carmines parents, not convinced of...Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Highway Safety Exercises 4150 are based on the...Ch. 8.1 - Prob. 46E Ch. 8.1 - Highway Safety Exercises 4150 are based on the...Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Highway Safety Exercises 4150 are based on the...Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.1 - Prob. 53E Ch. 8.1 - Prob. 54E Ch. 8.1 - Prob. 55E Ch. 8.1 - Prob. 56E Ch. 8.1 - Prob. 57E Ch. 8.1 - Prob. 58E Ch. 8.1 - Prob. 59E Ch. 8.1 - Give an example of a real-life situation that can...Ch. 8.1 - Prob. 61E Ch. 8.1 - Prob. 62E Ch. 8.1 - Prob. 63E Ch. 8.1 - Prob. 64E Ch. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - Prob. 6E Ch. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - Prob. 9E Ch. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - Prob. 14E Ch. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - In Exercises 19 and 20, graph the histogram of the...Ch. 8.2 - In Exercises 19 and 20, graph the histogram of the...Ch. 8.2 - In Exercises 21 and 22, graph the histogram of the...Ch. 8.2 - Prob. 22E Ch. 8.2 - Internet Addiction The probability that a randomly...Ch. 8.2 - 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Prob. 54E Ch. 8.3 - Compute the mean, median, and mode of the data...Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Compute the mean, median, and mode of the data...Ch. 8.3 - Compute the mean, median, and mode of the data...Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Compute the mean, median, and mode of the data...Ch. 8.3 - Prob. 9E Ch. 8.3 - Give a sample of five scores with mean 100 and...Ch. 8.3 - In Exercises 1116, calculate the expected value of...Ch. 8.3 - In Exercises 1116, calculate the expected value of...Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - In Exercises 1116, calculate the expected value of...Ch. 8.3 - In Exercises 1116, calculate the expected value of...Ch. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Stock Market Gyrations Following is a sample of...Ch. 8.3 - Stock Market Gyrations Following is a sample of...Ch. 8.3 - Gold The following figures show the price of gold...Ch. 8.3 - Silver The following figures show the price of...Ch. 8.3 - Supermarkets A survey of 52 U.S. supermarkets...Ch. 8.3 - Video Arcades Your company, Sonic Video, Inc., has...Ch. 8.3 - School Enrollment The following table shows the...Ch. 8.3 - School Enrollment Repeat Exercise 35, using the...Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - 2010 Income Distribution up to $100,000 The...Ch. 8.3 - 2003 Income Distribution up to $100,000 Repeat...Ch. 8.3 - Prob. 41E Ch. 8.3 - Prob. 42E Ch. 8.3 - Prob. 43E Ch. 8.3 - Prob. 44E Ch. 8.3 - Roulette A roulette wheel has the numbers 1...Ch. 8.3 - Roulette A roulette wheel has the numbers 1...Ch. 8.3 - Prob. 47E Ch. 8.3 - Prob. 48E Ch. 8.3 - Prob. 49E Ch. 8.3 - Spiders Your pet tarantula, Spider, has a .12...Ch. 8.3 - Exercises 51 and 52 assume familiarity with...Ch. 8.3 - Exercises 51 and 52 assume familiarity with...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Prob. 57E Ch. 8.3 - Prob. 58E Ch. 8.3 - Prob. 59E Ch. 8.3 - Insurance The Blue Sky Flight Insurance Company...Ch. 8.3 - Prob. 61E Ch. 8.3 - Prob. 62E Ch. 8.3 - Prob. 63E Ch. 8.3 - Prob. 64E Ch. 8.3 - Prob. 65E Ch. 8.3 - Prob. 66E Ch. 8.3 - Prob. 67E Ch. 8.3 - Prob. 68E Ch. 8.3 - Slim tells you that the population mean is just...Ch. 8.3 - Prob. 70E Ch. 8.3 - Prob. 71E Ch. 8.3 - Prob. 72E Ch. 8.3 - Prob. 73E Ch. 8.3 - Prob. 74E Ch. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - Prob. 11E Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - Prob. 13E Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - In Exercises 1524, calculate the expected value,...Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - In Exercises 1524, calculate the expected value,...Ch. 8.4 - In Exercises 1524, calculate the expected value,...Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Popularity Ratings In your bid to be elected class...Ch. 8.4 - Popularity Ratings Your candidacy for elected...Ch. 8.4 - Unemployment Following is a sample of unemployment...Ch. 8.4 - Unemployment Following is a sample of unemployment...Ch. 8.4 - Stock Market Gyrations Following is a sample of...Ch. 8.4 - 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Prob. 51E Ch. 8.4 - Prob. 52E Ch. 8.4 - Prob. 53E Ch. 8.4 - Prob. 54E Ch. 8.4 - Distribution of Wealth If we model after-tax...Ch. 8.4 - Prob. 56E Ch. 8.4 - Prob. 57E Ch. 8.4 - Prob. 58E Ch. 8.4 - Prob. 59E Ch. 8.4 - Distribution of Wealth If we model after-tax...Ch. 8.4 - Prob. 61E Ch. 8.4 - Prob. 62E Ch. 8.4 - Prob. 63E Ch. 8.4 - Prob. 64E Ch. 8.4 - Prob. 65E Ch. 8.4 - Prob. 66E Ch. 8.4 - Prob. 67E Ch. 8.4 - Prob. 68E Ch. 8.4 - Prob. 69E Ch. 8.4 - Prob. 70E Ch. 8.4 - Prob. 71E Ch. 8.4 - Prob. 72E Ch. 8.4 - Prob. 73E Ch. 8.4 - Prob. 74E Ch. 8.4 - Prob. 75E Ch. 8.4 - Prob. 76E Ch. 8.4 - Prob. 77E Ch. 8.4 - Prob. 78E Ch. 8.4 - Prob. 79E Ch. 8.4 - Prob. 80E Ch. 8.5 - In Exercises 18, Z is the standard normal...Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - In Exercises 18, Z is the standard normal...Ch. 8.5 - In Exercises 18, Z is the standard normal...Ch. 8.5 - Prob. 6E Ch. 8.5 - Prob. 7E Ch. 8.5 - Prob. 8E Ch. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - Prob. 11E Ch. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - Prob. 13E Ch. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - Find the probability that a normal variable takes...Ch. 8.5 - Find the probability that a normal variable takes...Ch. 8.5 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - Prob. 19E Ch. 8.5 - Suppose X is a normal random variable with mean...Ch. 8.5 - Suppose X is a normal random variable with mean...Ch. 8.5 - Prob. 22E Ch. 8.5 - If you roll a die 100 times, what is the...Ch. 8.5 - If you roll a die 100 times, what is the...Ch. 8.5 - If you roll a die 200 times, what is the...Ch. 8.5 - Prob. 26E Ch. 8.5 - SAT Scores SAT test scores are normally...Ch. 8.5 - Prob. 28E Ch. 8.5 - LSAT Scores LSAT test scores are normally...Ch. 8.5 - LSAT Scores LSAT test scores are normally...Ch. 8.5 - Prob. 31E Ch. 8.5 - Prob. 32E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - SAT Scores SAT test scores are normally...Ch. 8.5 - LSAT Scores LSAT test scores are normally...Ch. 8.5 - Baseball The mean batting average in major league...Ch. 8.5 - Baseball The mean batting average in major league...Ch. 8.5 - Prob. 39E Ch. 8.5 - Marketing Your hot sauce company rates its sauce...Ch. 8.5 - Prob. 41E Ch. 8.5 - Prob. 42E Ch. 8.5 - Prob. 43E Ch. 8.5 - Prob. 44E Ch. 8.5 - Distribution of Income If we model after-tax...Ch. 8.5 - Prob. 46E Ch. 8.5 - Prob. 47E Ch. 8.5 - Prob. 48E Ch. 8.5 - Prob. 49E Ch. 8.5 - Prob. 50E Ch. 8.5 - Prob. 51E Ch. 8.5 - Prob. 52E Ch. 8.5 - Prob. 53E Ch. 8.5 - Prob. 54E Ch. 8.5 - Prob. 55E Ch. 8.5 - Prob. 56E Ch. 8.5 - Prob. 57E Ch. 8.5 - Prob. 58E Ch. 8.5 - Aviation The probability of a plane crashing on a...Ch. 8.5 - Prob. 60E Ch. 8.5 - Prob. 61E Ch. 8.5 - Prob. 62E Ch. 8.5 - Prob. 63E Ch. 8.5 - Prob. 64E Ch. 8.5 - Prob. 65E Ch. 8.5 - Prob. 66E Ch. 8.5 - Prob. 67E Ch. 8.5 - Prob. 68E Ch. 8.5 - Prob. 69E Ch. 8.5 - Prob. 70E Ch. 8.5 - Prob. 71E Ch. 8.5 - Prob. 72E Ch. 8.5 - Prob. 73E Ch. 8.5 - Prob. 74E Ch. 8 - In Exercises 16, find the probability distribution...Ch. 8 - Prob. 2RE Ch. 8 - Prob. 3RE Ch. 8 - Prob. 4RE Ch. 8 - In Exercises 16, find the probability distribution...Ch. 8 - Prob. 6RE Ch. 8 - Prob. 7RE Ch. 8 - Prob. 8RE Ch. 8 - Prob. 9RE Ch. 8 - Prob. 10RE Ch. 8 - Prob. 11RE Ch. 8 - Prob. 12RE Ch. 8 - Prob. 13RE Ch. 8 - Prob. 14RE Ch. 8 - Prob. 15RE Ch. 8 - A die is constructed in such a way that rolling a...Ch. 8 - Prob. 17RE Ch. 8 - Prob. 18RE Ch. 8 - Prob. 19RE Ch. 8 - Prob. 20RE Ch. 8 - Prob. 21RE Ch. 8 - Prob. 22RE Ch. 8 - Prob. 23RE Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - Prob. 26RE Ch. 8 - Prob. 27RE Ch. 8 - Prob. 28RE Ch. 8 - Prob. 29RE Ch. 8 - Prob. 30RE Ch. 8 - Prob. 31RE Ch. 8 - In Exercises 2934 the mean and standard deviation...Ch. 8 - Prob. 33RE Ch. 8 - Prob. 34RE Ch. 8 - Prob. 35RE Ch. 8 - Prob. 36RE Ch. 8 - Prob. 37RE Ch. 8 - Prob. 38RE Ch. 8 - Prob. 39RE Ch. 8 - Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Prob. 47RE Ch. 8 - Prob. 48RE Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 1CS Ch. 8 - Prob. 2CS Ch. 8 - Prob. 3CS Ch. 8 - Prob. 4CS Ch. 8 - Which of the following lists of data would you...Ch. 8 - Prob. 6CS Ch. 8 - Prob. 7CS Ch. 8 - Prob. 8CS

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Whether the following distribution of first digits of Good neighbor, Inc.’s tax returns with a sample size of n = 1000 fails, with 95 % certainty, to follow Benford’s law: y 1 2 3 4 5 6 7 8 9 P ( Y = y ) 0.31 0.16 0.13 0.11 0.07 0.07 0.05 0.06 0.04

Solution Summary: The author explains that the distribution of first digits of Good neighbor, Inc.’s tax returns with a sample size of n=1000 fails to follow Benford's law.

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Whether the following distribution of first digits of Good neighbor, Inc.’s tax returns with a sample size of n=1000 fails, with 95% certainty, to follow Benford’s law:

y 1 2 3 4 5 6 7 8 9

P(Y=y) 0.31 0.16 0.13 0.11 0.07 0.07 0.05 0.06 0.04

Chapter 8 Solutions

Whether the following distribution of first digits of Good neighbor, Inc.’s tax returns with a sample size of n = 1000 fails, with 95 % certainty, to follow Benford’s law: y 1 2 3 4 5 6 7 8 9 P ( Y = y ) 0.31 0.16 0.13 0.11 0.07 0.07 0.05 0.06 0.04

Solution Summary: The author explains that the distribution of first digits of Good neighbor, Inc.’s tax returns with a sample size of n=1000 fails to follow Benford's law.

Concept explainers

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Whether the following distribution of first digits of Good neighbor, Inc.’s tax returns with a sample size of n=1000 fails, with 95% certainty, to follow Benford’s law: y 1 2 3 4 5 6 7 8 9 P(Y=y) 0.31 0.16 0.13 0.11 0.07 0.07 0.05 0.06 0.04

Chapter 8 Solutions

Whether the following distribution of first digits of Good neighbor, Inc.’s tax returns with a sample size of n=1000 fails, with 95% certainty, to follow Benford’s law:

y 1 2 3 4 5 6 7 8 9

P(Y=y) 0.31 0.16 0.13 0.11 0.07 0.07 0.05 0.06 0.04