Benford\'s Law claims that numbers chosen from very large data files tend to hav

Question

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 us say you took a random sample of n = 287 numerical entries from the file and r = 73 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 alpha = 0.1. Are the data statistically significant at the significance level? Based on your answers, will you reject or fail to reject the null hypothesis?

Explanation / Answer

phat= 131/499 = 0.2625251

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(0.2625251-0.301)/sqrt(0.301*(1-0.301)/499)

= -1.873725

Answer: -1.874

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