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 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* = 218
numerical entries from the file and *r* = 52 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.

(i) Test the claim that *p* is less than 0.301. Use
*α* = 0.05

1. What is the value of the sample test statistic? (Round your answer to two decimal places.)

2. Find the *P*-value of the test statistic. (Round your
answer to four decimal places.)

Answer #1

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....

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...

Fraudulent numbers in tax returns, payment records, invoices,
etc. often display patterns that aren’t present in legitimate
records. It is a striking fact that the first digits of numbers in
legitimate records often have probabilities that follow the model
(known as Benford’s Law) partially shown in the following
probability distribution, where the random variable x is the first
digit of the number. x 1 2 3 4 5 6 7 8 9 P(x) 0.301 0.176 0.125 ?
0.079 0.067 0.058...

Please use C++. You will be provided with two files. The first
file (accounts.txt) will contain account numbers (10 digits) along
with the account type (L:Loan and S:Savings) and their current
balance. The second file (transactions.txt) will contain
transactions on the accounts. It will specifically include the
account number, an indication if it is a withdrawal/deposit and an
amount.
Both files will be pipe delimited (|) and their format
will be the following:
accounts.txt : File with bank account info...

The weak law of large numbers states that the mean of a sample
is a consistent estimator of the mean of the population. That is,
as we increase the sample size, the mean of the sample converges in
probability to the expected value of the distribution that the data
comes from, provided that expected value is finite. Consider a
numerical example, a Student t distribution with n = 5, the same as
we have already seen earlier in this module....

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