Question

An auto company claims that the fuel efficiency of its sedan has been substantially improved. A consumer advocate organization wishes to compare the fuel efficiencies of its sedan between the 2019 and 2021 models. Each of 12 drivers drove both the 2019 and 2021 models on a highway and the fuel efficiency was measured (in miles per gallon). The same driver drove the same path for both the models.

Driver
Model 1 2 3 4 5 6 7 8 9 10 11 12
2019 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8
2017 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6

Use the 0.1 level of significance to test the claim that the average fuel efficiency of the sedan has improved. Assume normal population.

Answer 1

We reject the Null and conclude that at α = 0.1, the is enough evidence to support th claim that miles per gallon has improved between 2017 and 2019

Explanation:

This is a paired t test:

H0 : μx - μy = 0

H1 : μx - μy > 0

The test statistic :

dbar / (Sd/√n)

d = Xi - Yi

d = 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2

dbar = Σd / n = 11.8 / 12 = 0.983

Sd = Σ(d - dbar)²/ (n - 1) = 1.685 (calculator)

Hence,

Test statistic = 0.983 / (1.685/√12)

Test statistic = 0.983 / 0.4864176

= 2.021

Using the test statistic score, we could obtain the Pvalue using the Pvalue FROM Tscore calculator :

Degree of freedom, df = n - 1 = 12 - 1 = 11

Pvalue(2.021, 11) = 0.03415

α = 0.1

Pvalue < α ; We reject the Null and conclude that at α = 0.1, the is enough evidence to support th claim that miles per gallon has improved between 2017 and 2019