Recall that Benford's Law claims that numbers chosen from very large data fles 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 fle, the probabity of getting a number with "1as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue hle contains millons of numbers in a large computer data bank. You draw a random sample of n = 229 numbers from this file and r 5 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 () Test the daim that p is more than 0.301. Use a - 0.10. (a) what is the level of signihcance? State the null and alternate hypotheses O Hp= 0.301; Hp>0.301 O Hg: P = 0.301; Hp<0.301 O H: p>0.301; Hp = 0.301 O H:p= 0.301; Hp-0.301 (b) what sampling distribution will you use? O The Student's t, since np >5 and ng> 5 O The standard normal, since np> 5 and ng > 5 O The Student's t, since np

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Chapter11: Data Analysis And Probability
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Recall that Benford's Law clalms 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 v
leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millons of numbers in a large computer data bank. You draw a random sample of n = 229 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.
large data file, the probability of getting a number with "1" as the
() Test the dalm that p is more than 0.301. Use a 0.10.
(a) what is the level of signifcance?
State the null and alternate hypotheses.
O Hg: p = 0.301; H p> 0.301
O Hgi P = 0.301; Hip< 0.301
O Hạ: p> 0.301; Hp- 0.301
O Ho: P= 0.301; H: p- 0.301
(b) what sampling distribution will you use?
O The Student's t, since np > 5 and ng > 5.
O The standard normal, since np > 5 and ng > 5.
O The Student's t, since np <5 and nq<5.
O The standard normal, since np <S and ng <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 Pvalue.
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Transcribed Image Text:Recall that Benford's Law clalms 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 v leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millons of numbers in a large computer data bank. You draw a random sample of n = 229 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. large data file, the probability of getting a number with "1" as the () Test the dalm that p is more than 0.301. Use a 0.10. (a) what is the level of signifcance? State the null and alternate hypotheses. O Hg: p = 0.301; H p> 0.301 O Hgi P = 0.301; Hip< 0.301 O Hạ: p> 0.301; Hp- 0.301 O Ho: P= 0.301; H: p- 0.301 (b) what sampling distribution will you use? O The Student's t, since np > 5 and ng > 5. O The standard normal, since np > 5 and ng > 5. O The Student's t, since np <5 and nq<5. O The standard normal, since np <S and ng <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 Pvalue. us O9I 8:31 hp 口 女 esc @ # $4 1 2 4 7 9.
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