Is there a significant difference in gas mileage of a car for regular unleaded a
ID: 3022799 • Letter: I
Question
Is there a significant difference in gas mileage of a car for regular unleaded and premium unleaded? To test this equation a research randomly selected 15 drivers for a study. They were to drive their cars for one month on a regular unleaded and for one month on a premium unleaded gasoline. The participants drove their own cars for this experiment. the average sample difference was 2.85 miles per gallon in favor of the premium unleaded, and all the sample standard deviation of difference was 1.9 miles per gallon. For a = .01, does this test show enough evidence for the researcher to conclude that there is a significant difference in mileage between regular unleaded and preimium gasolune? Assume the difference in gasoline mileage figures are normally distributed in the population.
Explanation / Answer
As mileages are normally distirbuted, we use z distribution.
Let
ud = the mean paired difference for the drivers
Formulating the null and alternative hypotheses,
Ho: ud = 0
Ha: ud =/ 0
As we can see, this is a two tailed test.
Thus, getting the critical z, as alpha = 0.01 ,
alpha/2 = 0.005
zcrit = +/- 2.575829304
Getting the test statistic, as
X = sample mean difference = 2.85
uo = hypothesized mean difference = 0
n = sample size = 15
s = standard deviation = 1.9
Thus, z = (X - uo) * sqrt(n) / s = 5.809475019
Also, the p value is
p = 6.2669*10^-9
As |z| > 2.5758, and P < 0.01, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence at 0.01 level that mileage between regular unleaded and preimium gasolune are different. [CONCLUSION]
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