Question 9.3 - In an experiment with t = 4 population means, consider the four linear combinations of those means. = - + + = + - = + + + = + - + a) Which of the four linear combinations are contrasts? b) Which pairs of contrasts are orthogonal? C) Suppose we have two contrasts: = + - - and = + + - Is testing : = 0 equivalent to testing : = 0 ? Justify your answer Question 9.6 - Refer to Example 8.6 9(below). The political action group was interested in determining regional differences in the public’s opinion concerning air pollution. Write a contrast in the four population means to answer each of the following questions.  a. Question 1: Is the proportion of people who thought the EPA’s standards are not stringent enough different for the people living in the East compared to the people living in the West?  b. Question 2: Is the proportion of people who thought the EPA’s standards are not stringent enough different for the people living in the Northeast compared to the people living in the other three regions?  c. Question 3: Is the proportion of people who thought the EPA’s standards are not stringent enough different for the people living in the Northeast compared to the people living in the Southeast?  d. Simultaneously test if the three contrasts are different from 0 using an a = .05 test.  e. Are the three contrasts mutually orthogonal?  Example 8.6 9 A political action group conducted a national opinion poll to evaluate the voting public’s opinion concerning whether the new EPA regulations on air pollution were stringent enough to protect the public’s health. The group was also interested in determining if there were regional differences in the public’s opinion concerning air pollution. For this poll, the country was divided into four geographical regions (NE, SE, MW, W). A random sample of 100 registered voters was obtained from each of six standard metropolitan statistical areas (SMSAs) located in each of the four regions. The data in Table 8.21 are the sample proportions, , of people who thought the EPA standards were not stringent enough for the 24 SMSAs. a. Is there a significant difference in the variability of the four region’s proportion? Use a = 5 . b. Transform the data using arcsin . c. Compute the sample means and sample standard deviations for the transformed data. Did the transformation yield a stabilization of the variances? Question 9.5 - In a study of 10 new procedures of iron supplement, nine contrasts in the mean iron level in the supplement were constructed by the quality control department for comparing various characteristics of the procedures. a. In order to achieve an experimentwise error rate of 0.05, what value should be selected for the value of b. What is the critical value for the F statistic for testing the nine contrasts if there were six samples of the supplement taken from each of the 10 procedures?\ Question 9.13 – Researchers conducted an experiment to c ...

1. Question 9.3 - In an experiment with t = 4 population means,
consider the four linear combinations of those means.
= - + +
= + -
= + + +
= + - +
a) Which of the four linear combinations are contrasts?
b) Which pairs of contrasts are orthogonal?
C) Suppose we have two contrasts:
= + - - and = + + -
Is testing : = 0 equivalent to testing : = 0 ? Justify your answer
Question 9.6 - Refer to Example 8.6 9(below). The political
action group was interested in determining regional differences
in the public’s opinion concerning air pollution. Write a
contrast in the four population means to answer each of the
following questions.
a. Question 1: Is the proportion of people who thought the
EPA’s standards are not stringent enough different for the
people living in the East compared to the people living in the
West?
b. Question 2: Is the proportion of people who thought the
EPA’s standards are not stringent enough different for the
people living in the Northeast compared to the people living in
the other three regions?
c. Question 3: Is the proportion of people who thought the
EPA’s standards are not stringent enough different for the
people living in the Northeast compared to the people living in
the Southeast?
d. Simultaneously test if the three contrasts are different from 0
using an a = .05 test.
e. Are the three contrasts mutually orthogonal?

2. Example 8.6 9
A political action group conducted a national opinion poll to
evaluate the voting public’s opinion concerning whether the
new EPA regulations on air pollution were stringent enough to
protect the public’s health. The group was also interested in
determining if there were regional differences in the public’s
opinion concerning air pollution. For this poll, the country was
divided into four geographical regions (NE, SE, MW, W). A
random sample of 100 registered voters was obtained from each
of six standard metropolitan statistical areas (SMSAs) located
in each of the four regions. The data in Table 8.21 are the
sample proportions, , of people who thought the EPA standards
were not stringent enough for the 24 SMSAs.
a. Is there a significant difference in the variability of the four
region’s proportion? Use a = 5 .
b. Transform the data using arcsin .
c. Compute the sample means and sample standard deviations
for the transformed data. Did the transformation yield a
stabilization of the variances?
Question 9.5 - In a study of 10 new procedures of iron
supplement, nine contrasts in the mean iron level in the
supplement were constructed by the quality control department
for comparing various characteristics of the procedures.
a. In order to achieve an experimentwise error rate of 0.05, what
value should be selected for the value of
b. What is the critical value for the F statistic for testing the
nine contrasts if there were six samples of the supplement taken
from each of the 10 procedures?
Question 9.13 – Researchers conducted an experiment to
compare the effectiveness of four new weight-reducing agents
to that of an existing agent. The researchers randomly divided a
random sample of 50 males into five equal groups, with

3. preparation A1 assigned to the first group, A2 to the second
group, and so on. They then gave a prestudy physical to each
person in the experiment and told him how many pounds
overweight he was. A comparison of the mean number of
pounds overweight for the groups showed no significant
differences. The researchers then began the study program, and
each group took the prescribed preparation for a fixed period of
time. The weight losses recorded at the end of the study period
are given here:
A1
12.4
10.7
11.9
11.0
12.4
12.3
13.0
12.5
11.2
13.1
A2
9.1
11.5

4. 11.3
9.7
13.2
10.7
10.6
11.3
11.1
11.7
A3
8.5
11.6
10.2
10.9
9.0
9.6
9.9
11.3
10.5

5. 11.2
A4
12.7
13.2
11.8
11.9
12.2
11.2
13.7
11.8
12.2
11.7
S
8.7
9.3
8.2
8.3
9.0
9.4

6. 9.2
12.2
8.5
9.9
The standard (existing) agent is labeled agent S, and the four
new agents are labeled,, , and . Run an analysis of variance to
determine whether there are significant differences among the
five weight-reducing agents. Use α = .05. Do any of the AOV
assumptions appear to be violated? What conclusions do you
reach concerning the mean weight loss achieved using the five
different agent?
Question 9.17 – Refer to exercise 9.13. Suppose the new
weight-loss agents were of the following forms:
Refer to Exercise 9.13. Suppose the new weight- loss agents
were of the following form:
A1: Drug therapy with exercise and counseling
A2: Drug therapy with exercise but no counseling
A3: Drug therapy with counseling but no exercise
A4: Drug therapy with no exercise and no counseling
Construct contrasts to make comparisons among the agent
means that will address the following:
a. Compare the mean for the standard agent to the average of
the means for the four new agents.
b. Compare the mean for the agents with counseling to those
without counseling. (Ignore the standard.)
c. Compare the mean for the agents with exercise to those
without exercise. (Ignore the standard.)
d. Compare the mean for the agents with counseling to the
standard.

7. Question 9.23 - Researchers conducted a study of the effects of
three drugs on the fat content of the shoulder muscles in
labrador retrievers. They divided 80 dogs at random into four
treatment groups. The dogs in group A were the untreated
controls, while groups B, C, and D received one of three new
heartworm medications in their diets. Five dogs randomly
selected from each of the four groups received varying lengths
of treatment from 4 months to 2 years. The percentage fat
content of the shoulder muscles was determined and is given
here.
Treatment
ExamTime
%Fat
A
4months
2.84
A
4months
2.49
A
4months
2.50
A
4months
2.42
A
4months
2.61
A
8months
2.23
A
8months
2.48
A

8. 8months
2.48
A
8months
2.23
A
8months
2.65
A
1year
2.30
A
1year
2.30
A
1year
2.38
A
1year
2.05
A
1year
2.13
A
2years
2.64
A
2years
2.56
A
2years
3.30
A
2years
2.19
A

9. 2years
2.45
B
4months
2.43
B
4months
1.85
B
4months
2.42
B
4months
2.73
B
4months
2.07
B
8months
2.83
B
8months
2.59
B
8months
2.53
B
8months
2.73
B
8months
2.26
B
1year
2.70
B

10. 1year
2.54
B
1year
2.70
B
1year
2.81
B
1year
2.70
B
2years
3.24
B
2years
3.71
B
2years
2.95
B
2years
3.01
B
2years
3.08
C
4months
1.95
C
4months
2.67
C
4months
2.23
C

11. 4months
2.31
C
4months
2.53
C
8months
2.32
C
8months
2.36
C
8months
2.46
C
8months
2.04
C
8months
2.30
C
1year
2.85
C
1year
2.75
C
1year
2.62
C
1year
2.50
C
1year
2.69
C

12. 2years
2.90
C
2years
3.02
C
2years
3.78
C
2years
2.96
C
2years
2.87
D
4months
3.21
D
4months
2.20
D
4months
2.32
D
4months
2.79
D
4months
2.94
D
8months
2.45
D
8months
2.49
D

13. 8months
2.95
D
8months
2.05
D
8months
2.31
D
1year
2.53
D
1year
2.73
D
1year
2.65
D
1year
2.84
D
1year
2.92
D
2years
2.91
D
2years
2.89
D
2years
3.21
D
2years
2.89
D

14. 2years
2.68
Under the assumptions that conditions for an AOV were met,
the researchers then computed an AOV to evaluate the
difference in mean percentage fat content for dogs under the
four treatments. The AOV computations did not takes into
account the length of time on the medication. The AOV is given
here.
a. Is there a significant difference in the mean fat content in the
four treatment groups? Use α = 5 .
b. Do any of the three treatments for heartworm appear to have
increased the mean fat content over the level in the control
group?
Question 9.27 – The paper “The effect of an endothelin-receptor
antagonist, bosentan, on blood pressure in patients with
essential hypertension’’ [1998, The New England Journal of
Medicine, 338:784 –790] discussed the contribution of bosentan
to blood pressure regulation in patients with essential
hypertension. The study involved 243 patients with mild-to-
moderate essential hypertension. After a placebo run-in period,
patients were randomly assigned to receive one of four oral
doses of bosentan (100, 500, or 1,000 mg once daily, or 1,000
mg twice daily) or a placebo. The blood pressure was measured
before treatment began and after a 4-week treatment period. The
primary end point of the study was the change in blood pressure
from the base line obtained prior to treatment to the blood
pressure at the conclusion of the 4-week treatment period. A
summary of the data is given in the following table.

15. Calculate Tukey's W .You need to have equal sample sizes
across your means
a. Which of the dose levels were associated with a significantly
greater reduction in the diastolic pressure in comparison to the
placebo? Use α = .05.
b. Why was it important to include a placebo treatment in the
study?
c. Using just the four treatments (ignore the placebo), construct
a contrast to test for an increasing linear trend in the size of the
systolic pressure reductions as the dose levels are increased.
See Exercise 9.25 for the method for creating such a contrast.
d. Use the SNK procedure to test for pairwise differences in the
mean systolic blood pressure reduction for the four treatment
doses. Use α = .05
e. The researchers referred to their study as a double-
blind study. Explain the meaning of this terminology.