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.> C | www.webassign.net/web/Student/Assignment-Responses/submit?dep=17598932 : Apps D Registration Holds control Panel in Wi BookmarksPhysics-BUS 1120 C 9 How Do l Change M -derivative Nelnet Campus Com EZTV TV Torrents 0 10. -5 points U 8.3.0U 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 numbesin a large computer file. Let us say you took a random sample of n- 216 numerical entries from the file and r-51 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 (i) Test the claim that p is less than 0.301. Use -0.0S (a) What is the level of significance? State the null and alternate hypotheses. O Ho: p = 0.301, HI : p > 0.301 Ho: p = 0.301, HI: p0.301 Ho: p = 0.301; H1: p # 0.301 Ho: p 5 The standard normal, since np 5 and nq The Student's t, since np 5 and nq 5 O The Student's t, since np > 5 and nq> 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.) ENG 1:22 AM US 12/8/2017 | Desktop ^

Explanation / Answer

Solution:

i. Level of significance, a =0.05

a. Null Hypothesis (Ho): p = 0.301

Alternative Hypothesis (Ha): p < 0.301

b. The standard normal since np and nq > 5.

Sample proportion, p’ = X/n = 51/216 = 0.236

Test Statistics

Z = (p’ – p)/ p (1 – p)/n

Z = (0.236 – 0.301)/0.301*(1 – 0.301)/216

Z = -2.08

c. Using z-tables, the p-value is

P [Z < -2.08] = 0.0188

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

Because p-value is less than 0.05.

e. There is sufficient evidence at the 0.05 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is less than 0.301.

ii. Yes. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts

iii. We have not proved Ho to be alse. Because our data leads us to reject the null hypothesis, more investigation is merited.

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