Question

An auto rental firm is using 15 identical motors that are adjusted to run at a fixed speed to test 3 different brands of gasoline. Each brand of gasoline is assigned to exactly 5 of the motors. Each motor runs on 10 gallons of gasoline until it is out of fuel. The following represents the total mileages obtained by the different motors: 4. Gas 1: 220 251 226 246 260 Gas 2: 244 235 232 242 225 Gas 3: 252 272 250238 256 (a) compute the average and the variance of each gas type (3pt) (b) Test the hypothesis that the average mileage obtained is not affected by the type of gas used. Use the 5 percent level of significance. (5pt)

Answer 1

a)

Groups	Count	Sum	Average	Variance
Gas 1	5	1203	240.6	287.8
Gas 2	5	1178	235.6	59.3
Gas 3	5	1268	253.6	150.8

b)

Null hypothesis : The average millage obtained is not affected by the type of gas used .

Alternative hypothesis: The average millage obtained is affected by the type of gas used.

Using ANOVA single factor in excel we get output as

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	863.3333	2	431.6667	2.600924	0.115249	3.885294
Within Groups	1991.6	12	165.9667
Total	2854.933	14

Decision :

F cal < F crit

i.e 2.60 < 3.89

So fail to reject the null hypothesis

Conclusion:

at 5% LOS, there is enough evidence that the average millage obtained is not affected by the type of gas used