Suppose you are considering buying a car for $28,000, Toyota 86 and Acura ILX. A

Question

Suppose you are considering buying a car for $28,000, Toyota 86 and Acura ILX. A fuel-economy study was conducted with one vehicle of each brand with the same driver and combined scenarios. The mileage performance was observed for 10 tanks of fuel in each car. The data are as follows (in miles per gallon):

Assume the data is normally distributed. Is there evidence to support the claim that the average in mileage performance is greater for an Acura ILX than for a Toyota 86? (Use =0.05).

https://drive.google.com/file/d/0B-TpYwbWgGmUOWI3djZEbDExZDg/view?usp=sharing

Explanation / Answer

a)
Hypothesis:

Null hypothesis: 1 - 2 <= 0
Alternative hypothesis: 1 - 2 > 0

b)
Test statistic:
x1 = 24.77 , x2 = 31.25 . s1 = 0.1418 , s2 = 1.2195 , n1=n2 = 10

SE = sqrt[(s1^2/n1) + (s2^2/n2)]
SE = sqrt[(0.1418^2/10) + (1.2195^2/10)]
= 0.3882
t = [ (x1 - x2) - d ] / SE
= [(24.77-31.25) - 0] / 0.3882
= -16.6905

c) p value is calculated using t = -16.6905 , df =18
p value= .00001.
Results are statistically significant.
d)
we reject the null hypothesis.

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