Question

In: Statistics and Probability

The effect of three different lubricating oils on fuel economy in diesel truck engines is being...

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.

Solutions

Expert Solution

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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