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* = 88 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.

(i) Test the claim that *p* is more than 0.301. Use
*α* = 0.10.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: *p* = 0.301;
*H*_{1}: *p* ≠ 0.301*H*_{0}:
*p* = 0.301; *H*_{1}: *p* >
0.301 *H*_{0}: *p* =
0.301; *H*_{1}: *p* <
0.301*H*_{0}: *p* > 0.301;
*H*_{1}: *p* = 0.301

(b) What sampling distribution will you use?

The standard normal, since *np* < 5 and *nq*
< 5.The Student's *t*, since *np* < 5 and
*nq* < 5. The standard normal,
since *np* > 5 and *nq* > 5.The Student's
*t*, since *np* > 5 and *nq* > 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.)

Sketch the sampling distribution and show the area corresponding to
the *P*-value.

(d) 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 *α*?

At the *α* = 0.10 level, we reject the null hypothesis
and conclude the data are statistically significant.At the
*α* = 0.10 level, we reject the null hypothesis and conclude
the data are not statistically
significant. At the *α* = 0.10 level,
we fail to reject the null hypothesis and conclude the data are
statistically significant.At the *α* = 0.10 level, we fail
to reject the null hypothesis and conclude the data are not
statistically significant.

(e) Interpret your conclusion in the context of the
application.

There is sufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is greater than 0.301.There is insufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is greater than 0.301.

(ii) If *p* is in fact larger than 0.301, it would seem
there are too many numbers in the file with leading 1's. Could this
indicate that the books have been "cooked" by artificially lowering
numbers in the file? Comment from the point of view of the Internal
Revenue Service. Comment from the perspective of the Federal Bureau
of Investigation as it looks for "profit skimming" by unscrupulous
employees.

Yes. There seems to be too many entries with a leading digit 1.No. There seems to be too many entries with a leading digit 1. No. There does not seem to be too many entries with a leading digit 1.Yes. There does not seem to be too many entries with a leading digit 1.

(iii) Comment on the following statement: If we reject the null
hypothesis at level of significance *α* , we have not proved
*H*_{0} to be false. We can say that the probability
is *α* that we made a mistake in rejecting
*H _{o}*. Based on the outcome of the test, would you
recommend further investigation before accusing the company of
fraud?

We have proved *H*_{0} to be false. Because our
data lead us to reject the null hypothesis, more investigation is
not merited.We have not proved *H*_{0} to be false.
Because our data lead us to accept the null hypothesis, more
investigation is not merited. We have not
proved *H*_{0} to be false. Because our data lead us
to reject the null hypothesis, more investigation is not merited.We
have not proved *H*_{0} to be false. Because our
data lead us to reject the null hypothesis, more investigation is
merited.

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 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 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....

Professor Jennings claims that only 35% of the students at Flora
College work while attending school. Dean Renata thinks that the
professor has underestimated the number of students with part-time
or full-time jobs. A random sample of 82 students shows that 37
have jobs. Do the data indicate that more than 35% of the students
have jobs? Use a 5% level of significance.
(a) State the null and alternate hypotheses. Options:
H0: μ = 0.35; H1: μ <
0.35
H0:...

Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
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graduated. Does this indicate that the population proportion of
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67%? Use a 10% level of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p = 0.67;
H1: p ≠
0.67H0:...

The U.S. Department of Transportation, National Highway Traffic
Safety Administration, reported that 77% of all fatally injured
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involved an intoxicated driver. Do these data indicate that the
population proportion of driver fatalities related to alcohol is
less than 77% in Kit Carson County? Use α = 0.10.
(a) What is the level of significance?
Answer: 0.10
State the null...

Professor Jennings claims that only 35% of the students at Flora
College work while attending school. Dean Renata thinks that the
professor has underestimated the number of students with part-time
or full-time jobs. A random sample of 76 students shows that 36
have jobs. Do the data indicate that more than 35% of the students
have jobs? Use a 5% level of significance.
What are we testing in this problem?
single mean
single proportion
(a) What is the level of...

Professor Jennings claims that only 35% of the students at Flora
College work while attending school. Dean Renata thinks that the
professor has underestimated the number of students with part-time
or full-time jobs. A random sample of 84 students shows that 40
have jobs. Do the data indicate that more than 35% of the students
have jobs? Use a 5% level of significance. What are we testing in
this problem? single mean single proportion (a) What is the level
of...

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