Responses submit dep 15306987 93 007 Recall that Benford\'s Law claims that numb

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Responses submit dep 15306987 93 007 Recall that Benford's Law claims that numbers chosen from very large d 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 probability of getting a number with "1" 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 219 numerical entries from the file andr 51 of the entries had a first nonzero digit of 1. Let present the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. (i Test the claim that p is less than o 301. use a o.05. (a) What is the level of significance? State the null and alternate hypotheses O Ho: P c 0.301: H1: p 0.301 Ho: p 0.301: H 1: P 0.301 Ho: p 0.301: H1: p o.301 Ho: p o 301: H1: p o.301 (b) what sampling distribution will you use? The standard normal, since np 5 and ng 5. The standard normal, since np s and ng 5. The student's t, since np c 5 and ng c 5. The student's t, since np 5 and ng 5. what is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the p-value of the test statistic. Round your answer to four decimal places. 0 9 O Type here to search

Explanation / Answer

(a) Level of significance = 0.05
The correct option is H0: p = 0.301; H1: p < 0.301

(b) The correct option is The standard normal, since np> 5 and nq >5
n = 219, p = 0.301 and q = 1 - 0.301 = 0.699

sample proportion = 51/219 = 0.233
Standard error = sqrt(p(1-p)/n) = sqrt(0.233(1-0.233)/219) = 0.0286
sample test statistic, z = (0.233 - 0.301)/0.0286 = -2.38

(d) p-value for z = -2.38 is 0.0087

Top right graph is correct option

At the alpha = 0.05, we reject the null hypothesis, and conclude that the data are statistically significant.

(e) First option is correct. There is enough evidence at the 0.05 level to conclude that the true proportion of numbers with a leading 1 is less than 0.301.

ii) No, The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.

iii) First option is correct. We have not proved H0 to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.

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