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Test of hypothesis using ANOVA

In a bumper test, three types of autos were deliberately crashed into a barrier at 5mph, and resulting damage was estimated. five test vehicles of each type were crashed.

Goliath Varmint Weasel
$1,600 $1,290 $1,090
$760 $1,400 $2,100
$880 $1,390 $1,830
$1,950 $1,850 $1,250
$1,220 $950 $1,920

Are the mean crash damages the same for these three vehicles?
state a null and alternative hypothesis
identify the test statistic used
Fc=3.885
F=.937
Perform an ANOVA at a=.05

Solution Preview

Please see the attached file.

We will use ANOVA to test the hypothesis

Goliath Varmint Weasel
1,600 1,290 1,090
760 1,400 2,100
880 1,390 1,830
1,950 1,850 1,250
1,220 950 1,920
Mean= M 1282 1376 1638
Standard deviation=sj 496.31 321.84 441.78
Sample size=nj= 5 5 5

k=no of samples= 3
Grand mean of all the three samples= 1432.00 =(5 * 1282 + 5 * 1376 + 5 * 1638 ) / (5+5+5)

Note(The calculations of mean and standard deviation have not been shown here)

1) Null and Alternative Hypothesis

Null Hypothesis: H0: M 1= M 2= M 3 ...

Solution Summary

The solution uses ANOVA to test hypothesis for difference between mean crash damages for three vehicles.

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