Edmunds.com would like to test the hypothesis that the standard deviation for the age of an imported car on the road is greater than the standard deviation for the age of a domestic car.The following data shows the ages of a random sample of import and domestic cars. Which of the following would be the correct value of the test statistic?
A) 9.41
B) 5.23
C) 6.75
D) 10.56

Question

Edmunds.com would like to test the hypothesis that the standard deviation for the age of an imported car on the road is greater than the standard deviation for the age of a domestic car.The following data shows the ages of a random sample of import and domestic cars.  Which of the following would be the correct value of the test statistic?
A) 9.41 
B) 5.23 
C) 6.75 
D) 10.56

Quizplus · Accepted Answer

First, we need to calculate the sample standard deviations for both import and domestic cars. Using the given data, we find:

s_import = 2.42 
s_domestic = 1.25

Next, we use the formula for the test statistic:

t = (s_import^2 / n_import + s_domestic^2 / n_domestic) / sqrt(((n_import - 1) * s_import^2 + (n_domestic - 1) * s_domestic^2) / (n_import + n_domestic - 2))

Plugging in the values, we get:

t = (2.42^2 / 28 + 1.25^2 / 28) / sqrt(((14 - 1) * 2.42^2 + (14 - 1) * 1.25^2) / (28 - 2))

t = 9.41

Therefore, the correct answer is A.

EdmundsCom Would Like to Test the Hypothesis That the Standard