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. At α = .10, the null hypothesis
A) should not be rejected.
B) should be rejected.
C) should be revised.
D) should not be tested.

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.  ​ At α = .10, the null hypothesis
A) should not be rejected. 
B) should be rejected. 
C) should be revised. 
D) should not be tested.

Quizplus · Accepted Answer

We need to perform a two-sample t-test to determine if there is a significant difference in the mean MPG of the two brands. Using a calculator or software, we can calculate the mean and standard deviation of the difference between the two samples as -5.5 and 2.56, respectively. We can then calculate the t-test statistic as: (mean difference - hypothesized difference) / (standard deviation / sqrt(sample size)) = (-5.5 - 0) / (2.56 / sqrt(8)) = -6.38. Using a t-distribution table with 14 degrees of freedom (8 + 8 - 2), we find a critical value of 1.761 for a one-tailed test with alpha = 0.10. Since -6.38 is less than -1.761, we reject the null hypothesis and conclude that there is a significant difference in the mean MPG between the two brands of automobiles.

Two Major Automobile Manufacturers Have Produced Compact Cars with Engines