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	31.2	31.6	22.0	29.7	30.6
Mid-Size	17.3	17.6	18.9	17.2	28.2
Full-Size	27.2	28.1	15.9	31.9	29.7
SUV	20.0	22.0	20.7	23.6	31.4

(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

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

• ......

.........................................

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
block	235.404	3	78.468	5.81	0.0108	3.4903
fuel type	230.398	4	57.5995	4.27	0.0224	3.2592
Error	162.006	12	13.5005
Total	627.808	19

SUMMARY	Count	Sum	Average	Variance
Compact	5	145.1	29.02	15.912
Mid-Size	5	99.2	19.84	22.303
Full-Size	5	132.8	26.56	38.698
SUV	5	117.7	23.54	21.188
87 Octane	4	95.7	23.925	40.9825
89 Octane	4	99.3	24.825	38.93583
91 Octane	4	77.5	19.375	6.9825
Ethanol 5%	4	102.4	25.6	43.68667
Ethanol 10%	4	119.9	29.975	1.8825

..................

p value for fuel type = 0.0224

p value < 0.05

and p avlue for vehicle type < 0.05

so,

• Fuel type means differ significantly and vehicle size is also a significant fact

• ..................................

...................

Level of significance	0.05
no. of treatments,k	5
DF error =N-k=	12
MSE	13.50050
t-critical value,t(α/2,df)	2.179

			confidence interval
population mean difference	critical value	lower limit	upper limit	result
µ1-µ4	-6.050	5.6608	-11.71	-0.39	means are different
µ3-µ4	-10.600	5.6608	-16.26	-4.94	means are different

• Ethanol 10% and 87 Octane

• Ethanol 10% and 91 Octane

.............................

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