Question

In this problem, assume that the distribution of
differences is approximately normal. *Note*: For degrees of
freedom *d*.*f*. not in the Student's *t* table, use
the closest *d*.*f*. that is *smaller*. In some
situations, this choice of *d*.*f*. may increase the
*P*-value by a small amount and therefore produce a slightly
more "conservative" answer.

Are America's top chief executive officers (CEOs)
really worth all that money? One way to answer this question is to
look at row *B*, the annual company percentage increase in
revenue, versus row *A*, the CEO's annual percentage salary
increase in that same company. Suppose a random sample of companies
yielded the following data:

*B***: Percent
increase**

**for company**26 23 27 18 6 4 21 37

*A***: Percent increase**

**for CEO**23 23 22 14 −4 19 15 30

Do these data indicate that the population mean percentage increase
in corporate revenue (row *B*) is different from the
population mean percentage increase in CEO salary? Use a 5% level
of significance. (Let *d* = *B* − *A*.)

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: μ* _{d}* > 0;

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that *d* has an
approximately normal distribution.The standard normal. We assume
that *d* has an approximately uniform
distribution. The Student's *t*. We
assume that *d* has an approximately uniform distribution.The
Student's *t*. We assume that *d* has an approximately
normal distribution.

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

(c) Find (or estimate) the *P*-value.

*P*-value > 0.5000.250 < *P*-value
< 0.500 0.100 < *P*-value <
0.2500.050 < *P*-value < 0.1000.010 < *P*-value
< 0.050*P*-value < 0.010

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?

Since the *P*-value ≤ α, we fail to reject
*H*_{0}. The data are statistically significant.Since
the *P*-value > α, we reject *H*_{0}. The data
are not statistically significant. Since the
*P*-value ≤ α, we reject *H*_{0}. The data are
statistically significant.Since the *P*-value > α, we fail
to reject *H*_{0}. The data are not statistically
significant.

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

Fail to reject *H*_{0}. At the 5% level
of significance, the evidence is insufficient to claim a difference
in population mean percentage increases for corporate revenue and
CEO salary.Fail to reject *H*_{0}. At the 5% level of
significance, the evidence is sufficient to claim a difference in
population mean percentage increases for corporate revenue and CEO
salary. Reject *H*_{0}. At the
5% level of significance, the evidence is insufficient to claim a
difference in population mean percentage increases for corporate
revenue and CEO salary.Reject *H*_{0}. At the 5% level
of significance, the evidence is sufficient to claim a difference
in population mean percentage increases for corporate revenue and
CEO salary.

Answer #1

*H*_{0}. At the 5% level of
significance, the evidence is insufficient to claim a difference in
population mean percentage increases for corporate revenue and CEO
salary

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
Are America's top chief executive officers (CEOs) really worth all
that money? One way to answer this question is to look at row
B, the annual...

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
Are America's top chief executive officers (CEOs) really worth all
that money? One way to answer this question is to look at row
B, the annual...

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
Are America's top chief executive officers (CEOs) really worth all
that money? One way to answer this question is to look at row
B, the annual...

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom d.f. not in the
Student's t table, use the closest d.f. that is smaller. In some
situations, this choice of d.f. may increase the P-value by a small
amount and therefore produce a slightly more "conservative"
answer.
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B represent the score in the fourth (and final) round, and let row
A represent...

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
Do professional golfers play better in their last round? Let row
B represent the score in the fourth (and final) round, and
let row A represent...

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom d.f. not in the
Student's t table, use the closest d.f. that is smaller. In some
situations, this choice of d.f. may increase the P-value by a small
amount and therefore produce a slightly more "conservative"
answer.
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In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom d.f. not in the
Student's t table, use the closest d.f. that is smaller. In some
situations, this choice of d.f. may increase the P-value by a small
amount and therefore produce a slightly more "conservative" answer.
In environmental studies, sex ratios are of great importance. Wolf
society, packs, and ecology have been studied extensively at
different locations in the U.S. and foreign...

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