A researcher collected data from a sample of cars produced in 1993. He wanted to

Question

A researcher collected data from a sample of cars produced in 1993. He wanted to know how different drive trains resulted in different highway miles per gallon (MPG): all wheel drive, front wheel drive, or rear wheel drive. All assumptions were met and he conducted a one-way ANOVA which was statistically significant at the 0.05 alpha level: F(2, 90) = 6.28, p = 0.0028.

Below are the results of his post-hoc analysis.

Given the Minitab Express output above, which pairs of drive trains are significantly different from one another at the 0.05 alpha level?

Grouping Information Using the Tukey Method and 95% Confidence Drive Train Type N Mean Grouping Front Wheel Drive 67 30.2388 A Rear Wheel Drive 16 26.3125 All Wheel Drive 10 25.800 Means that do not share a letter are significantly different. Tukey Simultaneous Tests for Differences of Means Difference of Levels Difference of Means SE of Difference 95% CI TValue Adjusted P-Value 4.439 Front Wheel Drive-All Wheel Drive 1.712 (0.359, 8.518) 2.59 0.0296 0.9657 Rear Wheel Drive-All Wheel Drive 0.512 0.25 0.0173 Rear Wheel Drive-Front Wheel Drive -3.926 2.79 Individual confidence level 98.07%

Explanation / Answer

in the Tukey method of 95% confidence ( alpha=0.05) the grouping of same letter are not significantly different.

so Rear whell and All whell has same letter B as grouping. so these two Rear-All are not different, But

Front wheel drive-Rear wheel drive and

Front whell -All wheel drive are significantly different pair.

Also Tukey simultaneous Tests of differences of means also suggest that p-value=0.0296 of difference of means of Front wheel -All wheel drive is less than alpha=0.05 and p-value=0.0173 of difference of means of Rear wheel drive-Front wheel drive is less than alpha=0.05

so these pairs are significanlty different from one another at 0.05 alpha level.

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