Question

The fuel efficiency, measured in miles per gallon, was measured for each of 12 cars when the cars where brand new. After exactly 5 years of use, the fuel efficiency of the same 12 cars was measured again. The data is in the following table. Mileage when New Mileage after 5 years Difference 16 15 1 27 24 3 17 17 0 33 29 4 28 25 3 24 22 2 18 16 2 22 20 2 20 21 -1 22 20 2 29 22 7 21 22 -1 a). Construct a 99% CI for the mean difference between initial fuel efficiency and the fuel efficiency after 5 years. b). Do the data give an evidence that there is no difference in fuel efficiency.

Answer 1

Part a

Confidence interval for difference between two population means of paired samples is given as below:

Confidence interval = Dbar ± t*SD/sqrt(n)

From given data, we have

Dbar = 2

Sd = 2.215646838

n = 12

df = n – 1 = 11

Confidence level = 99%

Critical t value = 3.1058

(by using t-table)

Confidence interval = Dbar ± t*SD/sqrt(n)

Confidence interval = 2 ± 3.1058*2.215646838/sqrt(12)

Confidence interval = 2 ± 1.9865

Lower limit = 2 - 1.9865 = 0.0135

Upper limit = 2 + 1.9865 = 3.9865

0.0135 < µd < 3.9865

Part b

Do the data give evidence that there is no difference in fuel efficiency?

Data do not give evidence that there is no difference in fuel efficiency because the above confidence interval does not contain the value zero.