Question

A researcher randomly selected 217 student cars at a community college and found that they had ages with a mean of 7.89 years and a standard deviation of 4.8 years.

The researcher then selected 152 faculty cars from the same community college and found that they had ages with a mean of 5.99 years and a standard deviation of 3.65 years.


Suppose that this sample data is used to test the claim that the ages of student cars are more variable than the age of faculty cars.

What is the test statistic for the test?

Answer 1

To test the claim that the ages of student cars are more variable than the age of faculty cars, we can use the F-test for two population variances, with the null hypothesis H0: σ1² ≤ σ2² and the alternative hypothesis Ha: σ1² > σ2², where σ1² is the variance of student cars and σ2² is the variance of faculty cars.

The test statistic for the F-test is given by:

F = s1² / s2²

where s1² is the sample variance of student cars and s2² is the sample variance of faculty cars.

We can calculate the sample variances from the given information:

s1² = 4.8² = 23.04
s2² = 3.65² = 13.3225

Plugging these values into the formula for the test statistic, we get:

F = s1² / s2² = 23.04 / 13.3225 = 1.731

Therefore, the test statistic for the test is 1.731.