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	30.4	29.7	16.0	30.0	29.8
Mid-Size	17.0	17.2	20.8	19.1	30.7
Full-Size	28.0	28.3	19.7	29.8	27.1
SUV	18.6	22.2	15.0	23.9	31.6

  Click 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 (Fuel Type)
Blocks (Vehicle Size)
Error
Total

Group	Mean	n	Std. Dev
87 Octane
89 Octane
91 Octane
Ethanol 5%
Ethanol 10%
Compact
Mid-Size
Full-Size
SUV
Total

(c) Choose the correct statement. Use α = 0.05.

• 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 differ significantly, but vehicle size is not a significant factor.

• Fuel type means do not differ significantly and vehicle size is not a significant factor.

(d) Which fuel types show a significant difference in average fuel economy? Use α = 0.05. (You may select more than one answer. Click the box with a check mark for the correct answer and click to empty the box for the wrong answer.)

• Ethanol 10% and 87 Octane

• Ethanol 5% and 89 Octane

• 87 Octane and 91 Octane

• Ethanol 10% and 91 Octane

Answer 1

a)

Fuel type is the treatment and vehicle size is the blocking factor.

b)

applying ANOVA:

Source	SS	df	MS	F	p-value
Treatments	296.472	4	74.1180	4.29	.0220
Blocks	143.990	3	47.9965	2.78	.0868
Error	207.208	12	17.2673
Total	647.670	19

	Mean	n	Std. Dev
87 Octane	23.5000	4	6.6863
89 Octane	24.3500	4	5.7726
91 Octane	17.8750	4	2.8088
Ethanol 5%	25.7000	4	5.2313
Ethanol 10%	29.8000	4	1.9442
Compact	27.1800	5	6.2556
Mid-Size	20.9600	5	5.6607
Full-Size	26.5800	5	3.9670
SUV	22.2600	5	6.2456
Total	24.2450	20	5.8385

c)

Fuel type means differ significantly, but vehicle size is not a significant factor.

d)

Ethanol 10% and 91 Octane