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x e Statistics and Probability , _ .> C | www.webassign.net/web/Student/Assignment-Responses/submit?dep:17481 399 : Apps D Registration Holds control Panel in Wir BookmarksPhysics-BUS 1120 C 9 How Do l Change M -derivative Nelnet Campus Cor EZTV TV Torrents 0 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-216 numerical entries from the file and r-52 of the entries had a first nonzero digit of 1, Let represent 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 0.301. Use = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: p0.301; HI, p # 0.301 Ho: p 0.301; HI, p 0.301 Ho: 0.301; His > 0.301 Ho: p 5. The standard normal, since np 5 and nq

Explanation / Answer

(a) Level of significance = 0.05

Null and alternate hypothesis are
H0: p = 0.301 H1: p < 0.301

b)
Sampling distribution - the standard normal since np>5 and nq>5

pcap = 52/216 = 0.2407

Test statistics, z = (0.2407 - 0.301)/sqrt(0.301*(1-0.301)/216) = -1.9321

c)
p-value = 0.0267

Figure C (i.e. shaded area in the left tail only)

d)
Reject null hypothesis
Option (A)

e) Option (A)

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