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 increasefor company |
26 | 25 | 23 | 18 | 6 | 4 | 21 | 37 |

A: Percent
increasefor CEO |
21 | 23 | 20 | 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;
*H*_{1}: *μ*_{d} >
0*H*_{0}: *μ*_{d} > 0;
*H*_{1}: *μ*_{d} =
0 *H*_{0}:
*μ*_{d} = 0; *H*_{1}:
*μ*_{d} < 0*H*_{0}:
*μ*_{d} = 0; *H*_{1}:
*μ*_{d} ≠ 0*H*_{0}:
*μ*_{d} ≠ 0; *H*_{1}:
*μ*_{d} = 0

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

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

Answer #1

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.
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.
At five weather stations on Trail Ridge Road in Rocky Mountain
National Park, the peak wind gusts (in miles per hour) for January
and April are...

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.
The artifact frequency for an excavation of a kiva in Bandelier
National Monument gave the following information.
Stratum
Flaked Stone
Tools
Nonflaked Stone
Tools
1
9
2...

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.
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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