The McLaren formula 1 team wants to assess 5 different new wing designs Wing T F

Question

The McLaren formula 1 team wants to assess 5 different new wing designs Wing T For each wing, they record 7 individual lap times and get the results (sample 1 47.3 1.1 mean and standard deviation) listed in the table. They believe that all wings 2 46.4 1.3 should produce the same variability in the lap times. (a) Test whether the different wing designs are essentially equally good, or whether some design(s) is/are different. Use a 95% significance level. (b) Wing 5 seems to be the best (lowest average lap time) Which of the other wings is it better than, to 95% significance?

Explanation / Answer

(a)

Here we need one way ANOVA. Hypotheses are:

H0: The different wing designs are essentially equally good.

Ha: The different wing designs are not essatially equally good.

Following is the output of one way ANOVA analysis:

Since p-value is less than 0.05 so we reject the null hypothesis. That is we cannot conclude that the different wing designs are essentially equally good.

(B)

Following are results of Post Hoc test:

Tukey HSD Post-hoc Test...
Group 1 vs Group 2: Diff=-0.9000, 95%CI=-2.7068 to 0.9068, p=0.6046
Group 1 vs Group 3: Diff=-1.6000, 95%CI=-3.4068 to 0.2068, p=0.1022
Group 1 vs Group 4: Diff=-1.8000, 95%CI=-3.6068 to 0.0068, p=0.0512
Group 1 vs Group 5: Diff=-2.2000, 95%CI=-4.0068 to -0.3932, p=0.0110
Group 2 vs Group 3: Diff=-0.7000, 95%CI=-2.5068 to 1.1068, p=0.7928
Group 2 vs Group 4: Diff=-0.9000, 95%CI=-2.7068 to 0.9068, p=0.6046
Group 2 vs Group 5: Diff=-1.3000, 95%CI=-3.1068 to 0.5068, p=0.2519
Group 3 vs Group 4: Diff=-0.2000, 95%CI=-2.0068 to 1.6068, p=0.9976
Group 3 vs Group 5: Diff=-0.6000, 95%CI=-2.4068 to 1.2068, p=0.8693
Group 4 vs Group 5: Diff=-0.4000, 95%CI=-2.2068 to 1.4068, p=0.9668

Difference between the group 1 and group 5 is signifcant. So it is better than wing 1.

SS DF Variance F P Between 21 4 5.25 3.866 0.0119 Within 40.74 30 1.358 Total 61.74 34

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