Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero di

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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 an auditor for a very large corporation. Therevenue report involves millions of numbers in a large computerfile. Let us say you took a random sampleof n = 218 numerical entries from thefile and r = 47 of the entries had afirst nonzero digit of 1. Let p represent thepopulation proportion of all numbers in the corporate file thathave a first nonzero digit of 1.---- Test the claim that p is less than 0.301.Use 𝛼 = 0.05.
(a) What is the level of significance?
(a2) State the null and alternate hypotheses.
(b) What sampling distribution will you use?
1 The standard normal, since np < 5and nq < 5.
2 The standard normal, since np > 5and nq > 5.
3 The Student's t,since np < 5 and nq <5.
4 The Student's t,since np > 5 and nq >5.
(b2) What is the value of the sample test statistic? (Round youranswer to two decimal places.)(c) Find the P-value of the test statistic. (Roundyour answer to four decimal places.)Sketch the sampling distribution and show the area corresponding tothe P-value.
(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis? Are the data statisticallysignificant at level 𝛼?
1 At the 𝛼 = 0.05 level, we reject the null hypothesisand conclude the data are statistically significant.
2 At the 𝛼 = 0.05 level, we reject the null hypothesisand conclude the data are not statisticallysignificant.
3 At the 𝛼 = 0.05 level, we fail to reject the nullhypothesis and conclude the data are statistically significant.
4 At the 𝛼 = 0.05 level, we fail to reject the nullhypothesis and conclude the data are not statisticallysignificant.