Recall that 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. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 222 numerical entries from the file and r = 50 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.
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301. This is our population proportion (p), which is the proportion of all numbers in the corporate file that have a first nonzero digit of 1. Second, we have a sample of n = 222 numerical entries from the file. This is our sample size. Third, in our sample, r = Show more…
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Recall that 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. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 218 numerical entries from the file and r = 48 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. 1. What is the value of the sample test statistic? (Round your answer to two decimal places.) 2. Find the P-value of the test statistic. (Round your answer to four decimal places.)
Supreeta N.
Madhur L.
According to Benford's law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below.Test for goodness-of-fit with the distribution described by Benford's law. $$\begin{array}{l|c|c|c|c|c|c|c|c|c} \hline \text { Leading Digit } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \begin{array}{l} \text { Benford's Law: Distribution } \\ \text { of Leading Digits } \end{array} & 30.1 \% & 17.6 \% & 12.5 \% & 9.7 \% & 7.9 \% & 6.7 \% & 5.8 \% & 5.1 \% & 4.6 \% \\ \hline \end{array}$$ Frequencies of leading digits from IRS tax files are 152,89,63,48,39,40 $28,25,$ and 27 (corresponding to the leading digits of $1,2,3,4,5,6,7,8,$ and $9,$ respectively, based on data from Mark Nigrini, who provides software for Benford data analysis). Using a 0.05 significance level, test for goodness-of-fit with Benford's law. Does it appear that the tax entries are legitimate?
Goodness-of-Fit and Contingency Tables
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