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Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero 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. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let 489 numerical entries from the file and r=128 us say you took a random sample of n = of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using a = 0.1. What is the alternate hypothesis? O H₁: p>0.301 H₁: p=0.301 H₁: p<0.301 O H₁: p=0.301 H₁: p≤0.301

Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero 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. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let 489 numerical entries from the file and r=128 us say you took a random sample of n = of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using a = 0.1. What is the alternate hypothesis? O H₁: p>0.301 H₁: p=0.301 H₁: p<0.301 O H₁: p=0.301 H₁: p≤0.301

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Benford's Law and Hypothesis Testing Example #### Understanding Benford's Law Benford's Law states that in very large sets of numerical data, the first non-zero digit is more likely to be small. Specifically, the number "1" appears as the first digit around 30.1% of the time. #### Scenario Description Imagine that you are an auditor for a large corporation, tasked with ensuring the accuracy of financial reports. The company's revenue report comprises millions of numerical entries stored in a large computer file. #### Sample Collection and Analysis You randomly select a sample of \( n = 489 \) numerical entries from the file and find that \( r = 128 \) entries have "1" as the first non-zero digit. Let's denote the population proportion of all numbers in the corporate file that have "1" as the first non-zero digit by \( p \). #### Hypothesis Test We need to test the claim that \( p \) is less than 0.301 using a significance level of \( \alpha = 0.1 \). What is the alternate hypothesis (\( H_1 \))? #### Hypothesis Options Select the correct alternate hypothesis: - \( H_1: p > 0.301 \) - \( H_1: p \ne 0.301 \) - \( H_1: p < 0.301 \) - \( H_1: p = 0.301 \) - \( H_1: p \le 0.301 \) Understanding this scenario helps in applying statistical concepts to real-world data analysis tasks such as auditing financial reports.
Transcribed Image Text:### Benford's Law and Hypothesis Testing Example #### Understanding Benford's Law Benford's Law states that in very large sets of numerical data, the first non-zero digit is more likely to be small. Specifically, the number "1" appears as the first digit around 30.1% of the time. #### Scenario Description Imagine that you are an auditor for a large corporation, tasked with ensuring the accuracy of financial reports. The company's revenue report comprises millions of numerical entries stored in a large computer file. #### Sample Collection and Analysis You randomly select a sample of \( n = 489 \) numerical entries from the file and find that \( r = 128 \) entries have "1" as the first non-zero digit. Let's denote the population proportion of all numbers in the corporate file that have "1" as the first non-zero digit by \( p \). #### Hypothesis Test We need to test the claim that \( p \) is less than 0.301 using a significance level of \( \alpha = 0.1 \). What is the alternate hypothesis (\( H_1 \))? #### Hypothesis Options Select the correct alternate hypothesis: - \( H_1: p > 0.301 \) - \( H_1: p \ne 0.301 \) - \( H_1: p < 0.301 \) - \( H_1: p = 0.301 \) - \( H_1: p \le 0.301 \) Understanding this scenario helps in applying statistical concepts to real-world data analysis tasks such as auditing financial reports.
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