Engineers are testing company fleet vehicle fuel economy (miles per gallon) perf
ID: 3207669 • 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?
87 Octane 89 Octane 91 Octane Ethanol 5% Ethanol 10%
Compact 27.9 30.6 19.7 29.2 29.4
Mid-Size 17.3 18.1 17.8 19.7 31.7
Full-Size 28.8 28.7 18.3 28.7 30.8
SUV 17.8 22.6 18.1 17.2 28.9
PictureClick here for the Excel Data File
(a) Choose the correct statement.
Fuel type is the blocking factor and vehicle size is the treatment.
Fuel type is the treatment and vehicle size is the blocking factor.
(b) Fill in the boxes. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)
Two-Factor ANOVA
Source SS df MS F p-value
Treatments (Vehicle Size)
Blocks (Fuel Type)
Error
Total
Group Mean n Std. Dev
87 Octane
89 Octane
91 Octane
Ethanol 5%
Ethanol 10%
Compact
Mid-Size
Full-Size
SUV
Total
Explanation / Answer
Perform the Two-Way ANOVA without replication in excel for the given data and you would get the following output -
-------------------------------------------------------
(a)
As we are testing the efficiency of the fuel type for different sizes, so fuel here is the blocking factor and size is the treatment.
So, Fuel type is the blocking factor and vehicle size is the treatment.
-------------------------------------------------------------------------------
b)
The tables can be filled using the ANOVA output obtained from excel as -
And, the second one as -
Note that from the excel output we have got the variance but we need the standard deviation to complete the second table. So, take the square root of the variances to get the standard deviation as shown above.
Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance Compact 5 136.8 27.36 19.253 Mid-Size 5 105.6 21.12 42.712 Full-Size 5 135.3 27.06 24.783 SUV 5 104.6 20.92 24.507 87 Octane 4 91.8 22.95 39.05667 89 Octane 4 100 25 32.80667 91 Octane 4 73.9 18.475 0.709167 Ethanol 5% 4 94.8 23.7 37.83333 Ethanol 10% 4 121.8 30.45 2.896667 ANOVA Source of Variation SS df MS F P-value F crit Rows 191.9055 3 63.9685 5.186565 0.015808 3.490295 Columns 297.018 4 74.2545 6.020554 0.006772 3.259167 Error 148.002 12 12.3335 Total 636.9255 19Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.