Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. The mean of the differences is
A) .5.
B) 1.5.
C) 2.0.
D) 2.5.

Question

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.  ​ The mean of the differences is
A) .5. 
B) 1.5. 
C) 2.0. 
D) 2.5.

Quizplus · Accepted Answer

To find the mean of the differences, we subtract each pair of values (Brand A minus Brand B) and take the average of those differences. The calculations are as follows:
(30 - 26) = 4
(32 - 25) = 7
(35 - 28) = 7
(31 - 27) = 4
(29 - 24) = 5
(33 - 26) = 7
(32 - 28) = 4
(34 - 27) = 7

Sum of differences = 41
Mean of differences = 41/8 = 5.125

However, we need to round to one decimal place since we are dealing with MPG. Therefore, the mean of the differences is 5.1, which is closest to Choice C (2.0).

Two Major Automobile Manufacturers Have Produced Compact Cars with Engines