Random samples of four different models of cars were selected and the gas mileag

Question

Random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below.

Model A: 23,25,24,26

Model B: 28,26,29,30

Model C: 30,28,32,27

Model D: 25, 26, 25, 28

1)the Sum of Squares (between groups) is:

2)the critical value of the test statistic is:

3)the observed value of the test statistic is:

4)the p value is:

5)the decision is:

None of the other choices is correct

Fail to reject null hypothesis, means are not different

Reject null hypothesis, means are not different

Reject null hypothesis, means are different

None of the other choices is correct

Fail to reject null hypothesis, means are not different

Reject null hypothesis, means are not different

Reject null hypothesis, means are different

Explanation / Answer

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

ANOVA table

Hence,

1) Sum of squares (Between groups) = 55.5

2) Critical value = 3.490 [Assuming 0.05 level of significance and rounded off to 3 decimal places]

3) Test statistic = 6.434 [Rounded off to 3 decimal places]

4) p - Value = 0.0076

5) Decision: Reject null hypothesis, means are different. Option D is correct.

Column n Mean Std. Dev. Std. Error Model A 4 24.5 1.2909944 0.64549722 Model B 4 28.25 1.7078251 0.85391256 Model C 4 29.25 2.2173558 1.1086779 Model D 4 26 1.4142136 0.70710678

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