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An investigator analyzed the leading digits from 799 checks issued by seven suspect companies. The frequencies were found to be 3, 11, 4, 53, 474, 194, 7, 23, and 30, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.10 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud? Leading Digit Actual Frequency Benford's Law: Distribution of Leading Digits 7 30.1% 17.6% 12.5% 53 9.7% 474 7.9% 194 6.7% 5.8% 23 5.1% 4.6%

An investigator analyzed the leading digits from 799 checks issued by seven suspect companies. The frequencies were found to be 3, 11, 4, 53, 474, 194, 7, 23, and 30, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.10 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud? Leading Digit Actual Frequency Benford's Law: Distribution of Leading Digits 7 30.1% 17.6% 12.5% 53 9.7% 474 7.9% 194 6.7% 5.8% 23 5.1% 4.6%

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 4BGP
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Leading_Digit    Actual_Frequency    Benford's_Law:
1    3    30.1
2    11    17.6
3    4    12.5
4    53    9.7
5    474    7.9
6    194    6.7
7    7    5.8
8    23    5.1
9    30    4.6

An investigator analyzed the leading digits from 799 checks issued by seven suspect companies. The frequencies were found to be 3, 11, 4, 53, 474, 194, 7, 23, and 30, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.10 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud? Leading Digit Actual Frequency Q Benford's Law: Distribution of Leading Digits 7 Determine the null and alternative hypotheses. H₂: H₁: Calculate the test statistic, ². x² = (Round to three decimal places as needed.) Calculate the P-value. P-value = State the conclusion. (Round to four decimal places as needed.) Ho. There 3 30.1% 2 11 17.6% C 4 12.5% 4 53 9.7% 5 474 7.9% ▼sufficient evidence to warrant rejection of the claim that the leading digits are from a population with a distribution that conforms to Benford's law. It 194 6.7% 5.8% that the checks are the result of fraud. 23 5.1% 9 30 4.6%
Transcribed Image Text:An investigator analyzed the leading digits from 799 checks issued by seven suspect companies. The frequencies were found to be 3, 11, 4, 53, 474, 194, 7, 23, and 30, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.10 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud? Leading Digit Actual Frequency Q Benford's Law: Distribution of Leading Digits 7 Determine the null and alternative hypotheses. H₂: H₁: Calculate the test statistic, ². x² = (Round to three decimal places as needed.) Calculate the P-value. P-value = State the conclusion. (Round to four decimal places as needed.) Ho. There 3 30.1% 2 11 17.6% C 4 12.5% 4 53 9.7% 5 474 7.9% ▼sufficient evidence to warrant rejection of the claim that the leading digits are from a population with a distribution that conforms to Benford's law. It 194 6.7% 5.8% that the checks are the result of fraud. 23 5.1% 9 30 4.6%
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