1. A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Automobiles were randomly subjected to treatments and the results of the experiment (in miles per gallon) are presented below. The five automobile types are suspected to introduce "Heterogeneity" as gasoline brands are expected to performance differently in different automobile types. The experimenter would prefer to remove any corruptive effect of heterogeneity to get clean results on Brands. Hence the analysis is performed in twophases.
|
GasolineBrands
|
Average
|
|
X
|
Y
|
Z
|
|
Automobile Type
|
A
|
...
|
...
|
...
|
23.67
|
|
B
|
...
|
...
|
...
|
20.33
|
|
C
|
...
|
...
|
...
|
25.00
|
|
D
|
...
|
...
|
...
|
27.00
|
|
E
|
...
|
...
|
...
|
32.33
|
|
Average
|
24.40
|
26.80
|
25.80
|
|
In Phase I of the analysis on the above data, the following partial ANOVA results were obtained.
|
Source
|
DF
|
SS
|
MS
|
F
|
|
GasolineBrand
|
|
14.5
|
|
|
|
Error
|
|
|
|
|
|
Total
|
14
|
267.3
|
|
|
a) Complete the aboveANOVATable.
b) What experimental design was considered for the analysis under PhaseI?
c) State the Null and Alternate Hypotheses. Customize your hypothesis to the business problem context (do not usegenericterms).
d) Determine Critical-value. Conduct a Critical-value based Hypothesis test (at α = 0.10). What is your decision on theHypothesistest?
e) State your conclusion (what meaning the decision under part 'd' carries in the problem context)
In phase II of the analysis of the test data, the following partial ANOVA results were obtained.
|
Source
|
DF
|
SS
|
MS
|
F
|
|
AutomobileType
|
|
|
|
|
|
GasolineBrand
|
|
14.5
|
|
|
|
Error
|
|
15.5
|
|
|
|
Total
|
14
|
267.3
|
|
|
f) Complete the aboveANOVATable.
g) What experimental design was considered for the analysis under PhaseII?
h) Is Hypothesis Test of user importance under Phase II any different from the one considered for PhaseI?
i) Is a Hypothesis Test on the factor "Automobile Type" needed? Why or why not?
j) Determine Critical-value. Conduct a Critical-Value based Hypothesis Test (at α = 0.10).
k) Is there a significant difference in the mean miles- per- gallon characteristics of the three brands of gasoline based on the Hypothesistest?
l) If so, which brand(s) are different from the rest? (HINT: Use Fisher's LSDtest)
m) You own all five vehicles types in your fleet use them equally. You are interested in maximizing mpg for your vehicles. Which brand/s of Gasoline would you use and why?
n) Comparing analyses under Phase I and Phase II, what advantage Phase II provides if any over Phase Iofanalysis?
o) Which method among Phase I and Phase II provides the correct method of analysis in the problem context? Why orwhynot?