Explanation Given info: An investigator analyzed the leading digits of 784 checks given by seven companies. The table lists the observed frequencies for each of the leading digits starting from 1 to 9. LeadingDigits Observed Frequency 1 0 2 15 3 0 4 76 5 479 6 183 7 8 8 23 9 0 If the observed frequency do not agree with the expected frequency, then the fraud made in the check will be confirmed. The level of significance is 1%. Calculation: The claim is to test whether the leading digits in the issued checks are taken from a population distribution that confirms Benford’s law. If the claim is false, then the leading digits does not confirm with Benford’s law. The hypotheses are given below: Null hypothesis: H 0 : p 1 = 0.301 , p 2 = 0.176 , p 3 = 0.125 , p 4 = 0.097 , p 5 = 0.079 , p 6 = 0.067 , p 7 = 0.058 , p 8 = 0.051 , p 9 = 0.046 Alternative hypothesis: H 1 : At least one of the proportions is not equal to the given claim. The test statistic is calculated by the formula, χ 2 = ∑ ( O − E ) 2 E Where, O represents the observed frequency and E represents the expected frequency. Methods for finding the expected frequency: Method 1: If all the expected frequencies are equal, then E = n k . Method 2: If the expected frequencies are not equal, then E = n p for each category. Where, n is the total number of frequencies, k is the categories and p is the probability of occurrence. Here, the total frequency for theleading digits is 784 and there are 9 outcomes, then k is 9. Also, the probabilities are not equal. By using the second method, the expected frequencies are calculated as follows. For leading digit 1, E 1 = ( 784 ) ( 0.301 ) = 235.984 For leading digit 2, E 2 = ( 784 ) ( 0.176 ) = 137.984 For leading digit 3, E 3 = ( 784 ) ( 0.125 ) = 98 For leading digit 4, E 4 = ( 784 ) ( 0.097 ) = 76.048 For leading digit 5, E 5 = ( 784 ) ( 0.079 ) = 61.936 For leading digit 6, E 6 = ( 784 ) ( 0

Essentials of Statistics, Books a la Carte Edition (5th Edition)

5th Edition

ISBN: 9780321926739

Author: Mario F. Triola

Publisher: PEARSON

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Chapter 11.2, Problem 21BSC

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To test: The claim that the leading digits of the issued checks follow a population distribution that confirms Benford’s law.

To identify:The checks are fraud or not.

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Chapter 11.2, Problem 20BSC

Chapter 11.2, Problem 22BSC

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Essentials of Statistics, Books a la Carte Edition (5th Edition)

Ch. 11.2 - Prob. 1BSC Ch. 11.2 - Prob. 2BSC Ch. 11.2 - Prob. 3BSC Ch. 11.2 - Prob. 4BSC Ch. 11.2 - Prob. 5BSC Ch. 11.2 - Prob. 6BSC Ch. 11.2 - In Exercises 5-20, conduct the hypothesis test and...Ch. 11.2 - In Exercises 5-20, conduct the hypothesis test and...Ch. 11.2 - Prob. 9BSC Ch. 11.2 - In Exercises 5-20, conduct the hypothesis test and...

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To test: The claim that the leading digits of the issued checks follow a population distribution that confirms Benford’s law. To identify: The checks are fraud or not.

Solution Summary: The author analyzes the leading digits of 784 checks given by seven companies. If the observed frequency does not agree with the expected frequency, the fraud will be confirmed.

Videos

To test: The claim that the leading digits of the issued checks follow a population distribution that confirms Benford’s law.

To identify:The checks are fraud or not.

Want to see the full answer?

Chapter 11 Solutions

To test: The claim that the leading digits of the issued checks follow a population distribution that confirms Benford’s law. To identify: The checks are fraud or not.

Solution Summary: The author analyzes the leading digits of 784 checks given by seven companies. If the observed frequency does not agree with the expected frequency, the fraud will be confirmed.

Videos

To test: The claim that the leading digits of the issued checks follow a population distribution that confirms Benford’s law. To identify:The checks are fraud or not.

Want to see the full answer?

Chapter 11 Solutions

To test: The claim that the leading digits of the issued checks follow a population distribution that confirms Benford’s law.

To identify:The checks are fraud or not.