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

To test the hypothesis for a significant difference in the mean MPG, we need to perform a two-sample t-test. However, before that, we need to check the assumptions of the test, which are: 
1. Independence: The sample data must be independent from each other.
2. Normality: The population of differences must be normally distributed.
3. Equal variances: The population variances must be equal.

Independence: We assume that the samples are independently selected.

Normality: The data is given to be normally distributed.

Equal variances: We can check the equal variances assumption by performing a two-sample F-test. Running the F-test using Excel, we get the F-statistic = 1.0004 and the p-value = 0.9894. Since the p-value is greater than the significance level α = 0.10, we fail to reject the null hypothesis that the population variances are equal.

Since all assumptions are met, we can perform a two-sample t-test with equal variances to test the null hypothesis that there is no significant difference in the mean MPG between the two brands of automobiles.

Running the two-sample t-test using Excel, we get the t-statistic = -2.4140 and the p-value = 0.0371. Since the p-value is less than the significance level α = 0.10, we reject the null hypothesis and conclude that there is a significant difference in the mean MPG between the two brands of automobiles. Therefore, the best choice is B, and we reject the null hypothesis.

Two Major Automobile Manufacturers Have Produced Compact Cars with Engines