Question

29)

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 / Model B / Model C / Model D
   26  /   27   /   20   /   28
   30  /   23   /   25   /   27
   25  /   26   /   25   /   21
   25  /   22   /   26   /   26

Test the claim that the four different models have the same population mean. Use a significance level of 0.05. Use the p-value method of hypothesis testing.

Answer 1

Given:

Random samples of four different models of cars were selected and the gas mileage of each car was measured.

Data summary:

Groups	count , N	Sum	Average	Std. Dev
Group 1	4	101	25.25	3.594
Group 2	4	105	26.25	2.9861
Group 3	4	97	24.25	2.2174
Group 4	4	99	24.75	1.893

ANOVA TABLE:

Source	df	SS	MS	F	P-value
Between groups	3	8.75	2.9167	0.3846	0.7661
Within groups	12	91.0018	7.5835
Total	15	99.7518

Hypothesis test:

The null and alternative hypothesis is

H0 : 1 = 2 = 3 = 4

Ha : At least two of means 1, 2, 3, 4 are not equal.

From the ANOVA table

P-value = 0.7661

Significance level, = 0.05

Since P-value is a greater than significance level 0.05, we fail to reject null hypothesis.

Conclusion: Faill to reject H0. There is insufficient evidence to conclude that the four different models have the same population mean.