The effect of two factors---perehamber volume ratio (V) and injection timing (T)

Question

The effect of two factors---perehamber volume ratio (V) and injection timing (T) on the parts per million of noxious gas emitted from an engine was studied. The volume ratio was set at three squispaced levels and the time was also set at three squispaced levels. Two engines were built for each of the nine treatment combinations and the amount of the gas emitted was recorded for the 18 engines as shown in the Table (T Volume Time Low 6.27 5.43 6.94 6.51 7.22 7.05 Medium 8.08 8.04 7.48 7.52 8.65 8.97 7.34 7.87 8.61 8.32 9.02 9.07 Short Medium Long a) b) c) d) Test the effect of volume Test the effect of time Test the effect of the interaction Plot the interaction effect

Explanation / Answer

a) p-value of voume is 2.59 *10^(-6 ) << 0.05

hence it is significant

b) p-value of time is 0.000159 , which is also less than 0.05

hence it is significant too

c) p-value of interaction is

< 0.05

hence it is significant at 5 % level of significance

Anova: Two-Factor With Replication SUMMARY low medium high Total short Count 2 2 2 6 Sum 11.7 16.12 15.21 43.03 Average 5.85 8.06 7.605 7.171667 Variance 0.3528 0.0008 0.14045 1.188297 medium Count 2 2 2 6 Sum 13.45 15 16.93 45.38 Average 6.725 7.5 8.465 7.563333 Variance 0.09245 0.0008 0.04205 0.634987 long Count 2 2 2 6 Sum 14.27 17.62 18.09 49.98 Average 7.135 8.81 9.045 8.33 Variance 0.01445 0.0512 0.00125 0.88124 Total Count 6 6 6 Sum 39.42 48.74 50.23 Average 6.57 8.123333333 8.371667 Variance 0.4366 0.356186667 0.456697 ANOVA Source of Variation SS df MS F P-value F crit time 4.165833333 2 2.082917 26.9246 0.000159 4.256495 volumn 11.44103333 2 5.720517 73.94564 2.59E-06 4.256495 Interaction 1.385333333 4 0.346333 4.47684 0.028918 3.633089 Within 0.69625 9 0.077361 Total 17.68845 17

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