Answer:
Step-by-step explanation:
Corresponding fuel efficiencies of manufacturer A's car and manufacturer B's car form matched pairs.
The data for the test are the differences between the efficiencies of manufacturer A's car and manufacturer B's car
μd = fuel efficiency of manufacturer A's car minus the fuel efficiency of manufacturer B's car.
A B diff
32 28 4
27 22 5
26 27 - 1
26 24 2
25 24 1
29 25 4
31 28 3
25 27 - 2
Sample mean, xd
= (4 + 5 - 1 + 2 + 1 + 4 + 3 - 2)/8 = 2
xd = 2
Standard deviation = √(summation(x - mean)²/n
n = 8
Summation(x - mean)² = (4 - 2)^2 + (5 - 2)^2 + (- 1 - 2)^2 + (2 - 2)^2 + (1 - 2)^2 + (4 - 2)^2 + (3 - 2)^2 + (- 2 - 2)^2 = 44
Standard deviation = √(44/8
sd = 2.35
For the null hypothesis
H0: μd = 0
For the alternative hypothesis
H1: μd ≠ 0
This is a two tailed test and the distribution is a students t. Therefore, degree of freedom, df = n - 1 = 8 - 1 = 7
2) The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (2 - 0)/(2.35/√8)
t = 2.41
We would determine the probability value by using the t test calculator.
p = 0.047
Since alpha, 0.1 > the p value 0.047, then we would reject the null hypothesis. Therefore, at 1% significance level, we can conclude that there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.
