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	32.0	29.1	20.3	30.8	27.7
Mid-Size	18.1	19.7	18.9	19.9	27.7
Full-Size	27.0	27.2	20.9	31.4	31.7
SUV	22.2	19.1	21.1	18.4	31.7

(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

(c)	Choose the correct statement. Use α = 0.05.
	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 and vehicle size is not a significant factor. Fuel type means do not differ significantly, but vehicle size is a significant factor.

(d)	Which fuel types show a significant difference in average fuel economy? Use the Tukey simultaneous comparisons at α = 0.05.
	Ethanol 10% and 89 Octane Ethanol 5% and 87 Octane 89 Octane and 91 Octane Ethanol 10% and 91 Octane

Answer 1

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

Output using excel:

Anova: Two-Factor Without Replication
SUMMARY	Count, n	Sum	Mean	Variance	Standard deviation
Compact	5	139.9	27.98	21.107	4.594236
Mid-Size	5	104.3	20.86	15.128	3.889473
Full-Size	5	138.2	27.64	19.163	4.377556
SUV	5	112.5	22.5	28.765	5.363301
87 Octane	4	99.3	24.825	36.10917	6.00909
89 Octane	4	95.1	23.775	26.1825	5.116884
91 Octane	4	81.2	20.3	0.986667	0.993311
Ethanol 5%	4	100.5	25.125	48.03583	6.930789
Ethanol 10%	4	118.8	29.7	5.333333	2.309401
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Treatment	194.898	3	64.966	5.03	0.0175	3.490295
Blocks	181.607	4	45.402	3.51	0.0404	3.259167
Error	155.045	12	12.920
Total	531.550	19

c) Fuel type means differ significantly and vehicle size is also a significant factor.

(d) Tukey Hsd using excel:

Answer : Group 3 and 5 are significant. which are Ethanol 10% and 91 Octane

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