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.
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 recorded below.
Weather Station
1
2
3
4
5
January
137
120
126
64
78
April
108
115
102
88
61
Use 𝛼 = 0.01. (Let d =
January − April.)
What is the value of the sample test statistic? (Round
your answer to three decimal places.)
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.
In the following data pairs, A represents birth
rate and B represents death rate per 1000
resident population. The data are paired by counties in the
Midwest. A random sample of 16 counties gave the following
information.
A:
12.7
13.2
12.8
12.1
11.4
11.1
14.2
15.1
B:
9.8
14.5
10.5
14.4
13.2
12.9
10.9
10.0
A:
12.5
12.3
13.1
15.8
10.3
12.7
11.1
15.7
B:
14.1
13.6
9.1
10.2
17.9
11.8
7.0
9.2
Use 𝛼 = 0.01.
(Let d = A − B.)
What is the value of the sample test statistic? (Round
your answer to three decimal places.)
3:
Using techniques from an earlier section, we can find a
confidence interval for μd.
Consider a random sample of n matched data
pairs A, B.
Let d = B − A be
a random variable representing the difference between the values in
a matched data pair. Compute the sample mean d _
of the differences and the sample standard
deviation sd. If d has
a normal distribution or is mound-shaped, or
if n ≥ 30, then a confidence
interval for μd is
as follows.
B: Percent increase
for company
20
30
26
18
6
4
21
37
A: Percent
increase
for CEO
14
15
22
14
−4
19
15
30
(a) Using the data above, find a 95% confidence interval
for the mean difference between percentage increase in company
revenue and percentage increase in CEO salary. (Round your answers
to two decimal places.)
lower limit:
upper limit:
4:
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
20
18
8
18
6
4
21
37
A: Percent
increase
for CEO
26
21
27
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. Solve the problem using the
critical region method of testing.
(Let d = B − A. Round
your answers to three decimal places.)
test
statistic
=
critical
value
= ±
5:
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.
Suppose that 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 recorded below.
Wilderness District
1
2
3
4
5
January
139
124
122
64
78
April
100
111
113
88
61
Does this information indicate that the peak wind gusts
are higher in January than in April? Use 𝛼 =
0.01. Solve the problem using the critical region method of
testing. (Let d =
January − April. Round your answers to three decimal
places.)
test
statistic
=
critical
value
=