Recall that Benford\'s Law claims that numbers chosen from very large data files

Question

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 the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1.

(i) Test the claim that p is more than 0.301. Use = 0.05. (a) What is the level of significance?


State the null and alternate hypotheses.

H0: p = 0.301; H1: p 0.301 H0: p = 0.301; H1: p < 0.301     H0: p = 0.301; H1: p > 0.301 H0: p > 0.301; H1: p = 0.301

(b) What sampling distribution will you use?

The Student's t, since np > 5 and nq > 5. The Student's t, since np < 5 and nq < 5.     The standard normal, since np > 5 and nq > 5. The standard normal, 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.)


Sketch the sampling distribution and show the area corresponding to the P-value.

Explanation / Answer

a)level of significance :=0.05

H0: p = 0.301; H1: p > 0.301

b)

The standard normal, since np > 5 and nq > 5

here std error=(p(1-p)/n)1/2 =0.0305

phat=85/226=0.376

hence test stat z=(phat-p)/std error =(0.376-0.301)/0.0305=2.4615

c) for above right tailed tailed test p value on right tail =0.0069

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