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 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 = 222 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 α = 0.05.

(a) What is the level of significance?


State the null and alternate hypotheses.

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

(b) What sampling distribution will you use?

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


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

Answer 1

a).hypothesis:-

level of significance =0.05

b).the sampling distribution i will use is:-

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

[ np = (222*0.301 ) = 66.822 >5 and nq= 222*(1-0.301) =155.178 >5]

the sample test statistic :-

c) . p value be:-

[ in any blank cell of type =NORMSDIST(-2.32) press enter]

sampling distribution:-

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