Recall that Benford's Law claims that numbers chosen from verylarge data files tend to have "1" as the first nonzero digitdisproportionately often. In fact, research has shown that if yourandomly draw a number from a very large data file, the probabilityof getting a number with "1" as the leading digit is about 0.301.Now suppose you are the auditor for a very large corporation. Therevenue file contains millions of numbers in a large computer databank. You draw a random sample of n = 230 numbers from this fileand r = 88 have a first nonzero digit of 1. Let p represent thepopulation proportion of all numbers in the computer file that havea 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
State theALTERNATE 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 standard normal, since np > 5and nq > 5. The Student's t, since np < 5 and nq < 5. Thestandard normal, since np < 5 and nq < 5. What is the valueof the sample test statistic? (Round your answer to two decimalplaces.)

(c) Find the P-value of the test statistic. (Round your answerto four decimal places.)

(d) Sketch the sampling distribution and show the areacorresponding to the P-value.