In: Statistics and Probability
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.
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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