Question

To test if the mileage of three different makes of cars is the same, randomly selected trips on those makes are recorded and the data is shown below for the miles per gallon of the trips

Make 1	Make 2	Make 3
29.9	45.8	34.8
31.1	40.3	41.4
23.5	36.6	40
30.5	29	37.6
35.4	40.3	41.4
33	33	48.1
28.5	35.5	37.2
32.4	34.9	44.1
25.7	31	42
	40.3	44.9

Use one way ANOVA to test if the means of the mileage of the all the cars of these make are the same. Assume that the data may be treated as simple random samples.

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1. The verification that the ratio of the largest to the lowest of the standard deviations is less than 2.

2. There are no extreme outliers.

State the P_value and your conclusion
.

Answer 1

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Make 1	9	270	30	13.5475
Make 2	10	366.7	36.67	25.76011111
Make 3	10	411.5	41.15	15.75166667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	593.1057241	2	296.5528621	15.99709206	2.95567E-05	3.369016
Within Groups	481.986	26	18.53792308
Total	1075.091724	28

a)

highest sd = 25.76

lowest = 13.5475

highest/lowest = 25.76/13.5475 < 2

p-value = 2.95567*10^(-5) << 0.05

hence there is significant difference between groups