Question

The effect of three different lubricating oils on fuel economy in diesel truck engines is being studied. Fuel economy is measured using brake-specific fuel consumption after the engine has been running for 15 minutes. Five different truck engines are available for the study, and the experimenters conduct the following randomized complete block design.

                                                Truck

Oil               1               2             3              4                 5

1              0.502        0.634      0.491        0.329         0.512

2              0.534       0.675       0.520        0.435         0.540

3              0.513       0.595       0.489        0.400         0.511

(a) Analyze the data from this experiment.

(b) Use the Fisher LSD method to make comparisons among the three lubricating oils to determine specifically which oils differ in brake-specific fuel consumption.

Answer 1

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
1	5	2.468	0.4936	0.011805
2	5	2.704	0.5408	0.007421
3	5	2.508	0.5016	0.004856
1	3	1.549	0.516333	0.000264
2	3	1.904	0.634667	0.0016
3	3	1.5	0.5	0.000301
4	3	1.164	0.388	0.002917
5	3	1.563	0.521	0.000271

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
oil	0.006381	2	0.00319	5.899226	0.026658	4.45897
Columns	0.092001	4	0.023	42.52858	1.96E-05	3.837853
Error	0.004327	8	0.000541
Total	0.102708	14

F STAT for oil = 5.899

p value = 0.026

p value < 0.05,

so,  oils differ in brake-specific fuel consumption.

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

b)

Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	8
MSE	0.00054
t-critical value,t(α/2,df)	2.306

Fishers LSD critical value=tα/2,df √(MSE(1/ni+1/nj))

			confidence interval
population mean difference	critical value	lower limit	upper limit	result
µ1-µ2	-0.047	0.0339	-0.081	-0.013	means are different
µ1-µ3	-0.008	0.0339	-0.042	0.026	means are not different
µ2-µ3	0.039	0.0339	0.005	0.073	means are different

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