1. A research firm tests the miles-per-gallon characteristics of three brands of
ID: 2931115 • Letter: 1
Question
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 two phases.
Gasoline Brands
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
Gasoline Brand
14.5
Error
Total
14
267.3
a) Complete the above ANOVA Table.
b) What experimental design was considered for the analysis under Phase I?
c) State the Null and Alternate Hypotheses. Customize your hypothesis to the business problem context (do not use generic terms).
d) Determine Critical-value. Conduct a Critical-value based Hypothesis test (at = 0.10). What is your decision on the Hypothesis test?
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
Automobile Type
Gasoline Brand
14.5
Error
15.5
Total
14
267.3
f) Complete the above ANOVA Table.
g) What experimental design was considered for the analysis under Phase II?
h) Is a Hypothesis Test on the factor “Automobile Type” needed? Why or why not?
i) Is Hypothesis Test under Phase II (based on what the user is set out to find in the first place) any different from the one considered for Phase I?
j) Determine Critical-value. Conduct a Critical-Value based Hypothesis Test (at = 0.10).
k) Is there a significant difference in the mean miles- per- gallon characteristics of the three brands of gasoline based on the Hypothesis test?
l) If so, which brand(s) are different from the rest?
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 I of analysis?
o) Which method among Phase I and Phase II provides the correct method of analysis in the problem context? Why or why not?
Can you please tell me what to type in Excel to get these answers or if there are any formulas that could be used. I know this is very long but solving it would help me so much. I don't understand the concepts of the Phase I and Phase II. Hopefully this will help me.
Gasoline Brands
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
Explanation / Answer
(a)
gasoline df= 3-1=2, error df= total df - gasoline df
Error SS=Total SS - Gasoline SS=267.3-14.5=252.8
MS=SS/df
F=MS(gasoline)/MS(error)=0.34
(b) complete randomized design (CRD) one way Anova
(c) null hypothesis H0:all gasoline brand is same
alternate hypothesis H1: at lease one gasoline brand is different to another
(d) critical F(0.1,2,12)=2.81 ( using ms-excel =FINV(0.1,2,12))
(e) fail to reject H0 and conclude that all gasoline brand is same
(f)
(g) Randomized block design
(h) yes, this is one of the source of variation
(i) yes, there are two null hypothesis H0: all gasoline is same and another H0: all automobile is different
(j) please look part (f)
(k)yes, critical F is less than calculated F
(l) critical difference=sqrt(2*mse/r)*t(alpha,error df)=sqrt(2*1.9375/5)*t(0.1,8)=0.88*1.86=1.64
so brand Y is different from others
(m) ofcourse Y, its mean is highest
(n) Greater efficiency in an estimation sense also translates into greater power in testing for a treatment effect.
(o) phase II, blocking effect is estimated
Source DF SS MS F Gasoline Brand 2 14.5 7.25 0.34 Error 12 252.8 21.07 Total 14 267.3Related Questions
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