Engineers are testing company fleet vehicle fuel economy (miles per gallon) perf
ID: 3202534 • Letter: E
Question
Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?
rev: 03-04-2011
Fuel type is the treatment and vehicle size is the blocking factor.
Fuel type is the blocking factor and vehicle size is the treatment.
Fuel type means differ significantly but vehicle size is not a significant factor.
Fuel type means differ significantly and vehicle size is also a significant factor.
Fuel type means do not differ significantly but vehicle size is a significant factor.
Fuel type means do not differ significantly and vehicle size is not a significant factor.
87 Octane and 91 Octane.
Ethanol 10% and 91 Octane.
Ethanol 10% and 87 Octane.
Ethanol 5% and 91 Octane.
Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?
Explanation / Answer
Using Minitab:
ANOVA Table :
a ) Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Vehical size 3 235.4 78.47 5.81 0.011
Fuel type 4 230.4 57.60 4.27 0.022
Error 12 162.0 13.50
Total 19 627.8
The p-value for the vehicle size factor is given as 0.011. Since this is less than the chosen a-level of 0.05, it means the effect of vehicle size on tratment is significant.
The p-value for fuel type 0.022 is also less than 0.05, indicating that there is also a significant effect of fuel type on treatment.
Here Fuel type means differ significantly and vehicle size is also a significant factor.
Descriptive Statistics: Treatment
Total
Variable Vehical size Count Mean StDev
Treatment Compact 5 29.02 3.99
Full-Size 5 26.56 6.22
Mid-Size 5 19.84 4.72
SUV 5 23.54 4.60
Descriptive Statistics: Treatment
Total
Variable Fuel type Count Mean StDev
Treatment 87 Octane 4 23.93 6.40
89 Octane 4 24.83 6.24
91 Octane 4 19.38 2.64
Ethanol 10% 4 29.975 1.372
Ethanol 5% 4 25.60 6.61
Tukey Simultaneous Tests for Differences of Means
Difference SE of Adjusted
Difference of Levels of Means Difference 95% CI T-Value P-Value
89 Octane - 87 Octane 0.90 3.64 (-10.35, 12.15) 0.25 0.999
91 Octane - 87 Octane -4.55 3.64 (-15.80, 6.70) -1.25 0.724
Ethanol 10% - 87 Octane 6.05 3.64 ( -5.20, 17.30) 1.66 0.484
Ethanol 5% - 87 Octane 1.68 3.64 ( -9.57, 12.92) 0.46 0.990
91 Octane - 89 Octane -5.45 3.64 (-16.70, 5.80) -1.50 0.579
Ethanol 10% - 89 Octane 5.15 3.64 ( -6.10, 16.40) 1.41 0.628
Ethanol 5% - 89 Octane 0.77 3.64 (-10.47, 12.02) 0.21 0.999
Ethanol 10% - 91 Octane 10.60 3.64 ( -0.65, 21.85) 2.91 0.069
Ethanol 5% - 91 Octane 6.23 3.64 ( -5.02, 17.47) 1.71 0.457
Ethanol 5% - Ethanol 10% -4.38 3.64 (-15.62, 6.87) -1.20 0.750
Tukey Simultaneous Tests for Differences of Means
Difference SE of Adjusted
Difference of Levels of Means Difference 95% CI T-Value P-Value
89 Octane - 87 Octane 0.90 3.64 (-10.35, 12.15) 0.25 0.999
91 Octane - 87 Octane -4.55 3.64 (-15.80, 6.70) -1.25 0.724
Ethanol 10% - 87 Octane 6.05 3.64 ( -5.20, 17.30) 1.66 0.484
Ethanol 5% - 87 Octane 1.68 3.64 ( -9.57, 12.92) 0.46 0.990
91 Octane - 89 Octane -5.45 3.64 (-16.70, 5.80) -1.50 0.579
Ethanol 10% - 89 Octane 5.15 3.64 ( -6.10, 16.40) 1.41 0.628
Ethanol 5% - 89 Octane 0.77 3.64 (-10.47, 12.02) 0.21 0.999
Ethanol 10% - 91 Octane 10.60 3.64 ( -0.65, 21.85) 2.91 0.069
Ethanol 5% - 91 Octane 6.23 3.64 ( -5.02, 17.47) 1.71 0.457
Ethanol 5% - Ethanol 10% -4.38 3.64 (-15.62, 6.87) -1.20 0.750
The confidence intervals for the all pairs of means all include zero, which indicates that the differences are not significant.
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