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# Test of hypothesis using ANOVA

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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

https://brainmass.com/statistics/analysis-of-variance/test-of-hypothesis-using-anova-188381

#### Solution Preview

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.

\$2.49