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

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....

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....

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....

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.
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...

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...

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...

Benford's Law states that the first nonzero digits of numbers
drawn at random from a large complex data file have the following
probability distribution.† First Nonzero Digit 1 2 3 4 5 6 7 8 9
Probability 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046
Suppose that n = 275 numerical entries were drawn at random from a
large accounting file of a major corporation. The first nonzero
digits were recorded for the sample. First Nonzero Digit 1 2...

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