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 = 227 numbers from this file and r= 87 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. (1) Test the claim that p is more than 0.301. Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Hạ: p = 0.301; H,: p+ 0.301 О Hа р- 0.301; н,: р» 0.301 O Ho: P> 0.301; H: p = 0.301 O Hg: 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 Student's t, since np < 5 and ng < 5. O The standard normal, since np > 5 and ng > 5. O The standard normal, since np < 5 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.)
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 = 227 numbers from this file and r= 87 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. (1) Test the claim that p is more than 0.301. Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Hạ: p = 0.301; H,: p+ 0.301 О Hа р- 0.301; н,: р» 0.301 O Ho: P> 0.301; H: p = 0.301 O Hg: 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 Student's t, since np < 5 and ng < 5. O The standard normal, since np > 5 and ng > 5. O The standard normal, since np < 5 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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text: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 = 227 numbers from this file andr = 87 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.
(1) Test the claim that p is more than 0.301. Use a = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
O Họ: p = 0.301; H: p 0.301
O Ho: P = 0.301; H: p > 0.301
O Ho: P> 0.301; H: p = 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.
The Student's t, since np < 5 and ng < 5.
O The standard normal, since np > 5 and ng > 5.
O The standard normal, since np < 5 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.)
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