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 0.304. 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. Test the claim that p is more than 0.304. Use ? = 0.10. State the null hypothesis H0 and the alternate hypothesis H1. np? nq? What is the value of the sample test statistic? (Round your answer to two decimal places.) Find the P-value of the test statistic. (Round your answer to four decimal places.) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? Interpret your conclusion in the context of the application.
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 0.304. 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.
Test the claim that p is more than 0.304. Use ? = 0.10.
State the null hypothesis H0 and the alternate hypothesis H1.
np?
nq?
What is the value of the sample test statistic? (Round your answer to two decimal places.)
Find the P-value of the test statistic. (Round your answer to four decimal places.)
Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
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