show all work to get full credit write the pledge on top of your work
Search for question
Question
Show ALL WORK to get full credit.
(Write the pledge on top of your work and sign under it.)
Note: In your submission, you must do the following:
•
You can use a statistical software to get twoway ANOVA table. Besides the
ANOVA table, perform calculations manually and SHOW ALL STEPS of your
calculations to receive full credit.
Write down your answer in your own words by yourself.
Round all test statistics to four decimal places.
Problem 1:
The results of a comparison of four popular minivans are reported in the following table.
One of the features the researchers compared was the distance (in feet) required for the
minivan to come to a complete stop when traveling at a speed of 60 miles per hour
(braking distance). Suppose the braking distances were measured for five minivans of
each type with the following results.
Braking Distances (Feet)
Minivan A
150
152
151
149
153
Minivan B
153
150
156
151
155
Minivan C
Minivan D
155
167
150
164
157
169
158
162
155
173
a) The researcher wished to perform an Ftest to compare the average braking
distances for the four minivan models. What assumptions must the researcher
make to apply this test? Do the data appear to satisfy these assumptions? Explain.
b) Using the Ftest, can the researcher conclude at a = 0.10 that there is a
difference among average braking distances for the four minivan models?
Problem 2:
Solve Problem 1 using the Tukey's method. Compare the results to the results obtained
by using the Ftest. Problem 3:
Solve Problem 1 using the Bonferroni method. Compare the results to the results
obtained by using the Tukey's method.
Problem 4:
An Internet service provider is considering four different servers for purchase. Potentially,
the company would be purchasing hundreds of these servers, so it wants to make sure it
is making the best decision. Initially, five of each type of server are borrowed, and each is
randomly assigned to one of the 20 technicians (all technicians are similar in skill). Each
server is then put through a series of tasks and rated using a standardized test. The
higher the score on the test, the better the performance of the server. The data are as
follows.
Server Test Scores
Server 1
Server 2
Server 3
Server 4
48.5
56.4
52.1
64.3
46.5
68.2
56.3
68.3
52.4
68.5
48.3
72.2
54.1
64.2
52.2
70.6
58.9
60.1
54.8
56.5
Perform a KruskalWallis test on these data using a = 0.10. Are there differences
between the servers?
Problem 5:
The following table gives the survival times (in hours) for animals in an experiment
whose design consisted of three poisons, four treatments, and four observations per cell.
Poison
Treatment
A
B
C
D

3.1
4.5
8.2
11.0
4.3
4.5
4.5
7.1
4.6
4.3
8.8
7.2
6.3
7.6
6.6
6.2

3.6
2.9
9.2
6.1
4.4
3.5
5.6
10.0
4.0
2.3
4.9
12.4
3.1
4.0
7.1
3.8
III
2.2
2.1
3.0
3.7
2.3
2.5
3.0
3.6
1.8
2.3
3.8
2.9
2.4
2.2
3.1
3.3
Conduct a twoway analysis of variance to test the effects of the two main factors and
their interaction. Use α = 0.10.
Problem 6:
A banana grower has three fertilizers from which to choose. He would like to determine
which fertilizer produces banana trees with the largest yield (measured in pounds of bananas produced). The banana grower has noticed that there is a difference in the
average yields of the banana trees depending on which side of the farm they are planted
(South Side, North Side, West Side, or East Side). Because of the variation in yields
among the areas on the farm, the farmer has decided to randomly select three trees
within each area and then randomly assign the fertilizers to the trees. After harvesting
the bananas, he calculates the yields of the trees within each of the areas. The results are
as follows.
Banana Yields (Pounds)
Fertilizer A
Fertilizer B
Fertilizer C
South Side
53
51
58
North Side
48
47
53
West Side
50
48
56
East Side
50
47
54
a) Do you think a randomized block design is appropriate for the banana grower's
study? What assumptions must the banana grower make to apply this test? Do
the data appear to satisfy these assumptions? Explain.
b) Perform a twoway ANOVA using randomized block design. Use α = 0.10.
Problem 7:
Solve Problem 6 using the Friedman's Test. Compare the results to the results obtained
in Problem 6.