Exhibit 10-9
Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the 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 show the results of the test.
-Refer to Exhibit 10-9. At 90% confidence the null hypothesis
A)should not be rejected
B)should be rejected
C)should be revised
D)None of these alternatives is correct.

Question

Exhibit 10-9
Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the 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 show the results of the test. 
-Refer to Exhibit 10-9. At 90% confidence the null hypothesis
A)should not be rejected 
B)should be rejected 
C)should be revised 
D)None of these alternatives is correct.

Quizplus · Accepted Answer

To determine if there is a significant difference in the MPG of the two brands of automobiles, we need to conduct a two-sample t-test for the difference in means. Using the data provided in Exhibit 10-9, we calculate the mean MPG for Brand A as 28.75 and the mean MPG for Brand B as 24.5. The difference in means is 4.25.

Using a two-sample t-test with a 90% confidence level, we find that the calculated t-value of 1.213 is less than the critical t-value of 1.860 (using a two-tailed test and 14 degrees of freedom). Therefore, we fail to reject the null hypothesis that there is no significant difference in the MPG of the two brands of automobiles at a 90% confidence level.

Thus, the correct choice is B, the null hypothesis should be rejected.

Exhibit 10-9 Two Major Automobile Manufacturers Have Produced Compact Cars with the with the Same