Question

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 = 230 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.

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 an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 216 numerical entries from the file and r = 51 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.

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.)

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.301
Alternative Hypothesis, Ha: p ≠ 0.301

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.3696 - 0.301)/sqrt(0.301*(1-0.301)/230)
z = 2.27

P-value Approach
P-value = 0.0232

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.301
Alternative Hypothesis, Ha: p ≠ 0.301

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.2361 - 0.301)/sqrt(0.301*(1-0.301)/216)
z = -2.08

P-value Approach
P-value = 0.0375