A researcher conducted an experiment to test the effects of running 3 different types of gasoline with 3 possible types of additive on the mileage obtained. The experiment assumed that there is an interaction between gasoline type and the type of additive, hence, a two-factor ANOVA was employed in the data analysis. It was decided to run 36 motors - 4 in each factor level combinations. The following are the analysis results MEAN

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A researcher conducted an experiment to test the effects of running 3 different
types of gasoline with 3 possible types of additive on the mileage obtained. The
experiment assumed that there is an interaction between gasoline type and the
type of additive,
hence, a two-factor ANOVA was employed in the data analysis. It was decided to
run 36 motors - 4 in each factor level combinations. The following are the
analysis results
MEAN
GAS TYPE 1
GAS TYPE 2
GAS TYPE 3
ADDITIVE 1
125.825
127
126.35
126.3917
ADDITIVE 2
130.775
133.6
132.5
132.2917
ADDITIVE 3
128.275
137.825
123
129.7
128.2917
132.8083
127.2833
129.4611
Analysis of Variance Table
Df
Sum Sq
Mean Sq
F Value
Pr(>F)
factor(gas.ty
2
207.7706
103.8853
11.08482
0.000306
pe)
factor(additi
2
209.8872
104.9436
11.19775
0.000287
ve)
factor(gas.ty
pe):factor(ad 4
ditive)
Residuals
262.9678
65.74194
7.01483
0.000523
27
|253.04
9.371852
NA
NA
a.) Is there a significant interaction between the type of gasoline and the type of additive?
Why?
b.) What does the result on the test for significant interaction imply?
c.) Say you are to choose between the three gasoline types, regardless of the type of additive
used and considering all other factors constant. Which gasoline would you prefer for your
motor and why?
Transcribed Image Text:A researcher conducted an experiment to test the effects of running 3 different types of gasoline with 3 possible types of additive on the mileage obtained. The experiment assumed that there is an interaction between gasoline type and the type of additive, hence, a two-factor ANOVA was employed in the data analysis. It was decided to run 36 motors - 4 in each factor level combinations. The following are the analysis results MEAN GAS TYPE 1 GAS TYPE 2 GAS TYPE 3 ADDITIVE 1 125.825 127 126.35 126.3917 ADDITIVE 2 130.775 133.6 132.5 132.2917 ADDITIVE 3 128.275 137.825 123 129.7 128.2917 132.8083 127.2833 129.4611 Analysis of Variance Table Df Sum Sq Mean Sq F Value Pr(>F) factor(gas.ty 2 207.7706 103.8853 11.08482 0.000306 pe) factor(additi 2 209.8872 104.9436 11.19775 0.000287 ve) factor(gas.ty pe):factor(ad 4 ditive) Residuals 262.9678 65.74194 7.01483 0.000523 27 |253.04 9.371852 NA NA a.) Is there a significant interaction between the type of gasoline and the type of additive? Why? b.) What does the result on the test for significant interaction imply? c.) Say you are to choose between the three gasoline types, regardless of the type of additive used and considering all other factors constant. Which gasoline would you prefer for your motor and why?
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