An insurance company has conducted a study of its accident claim experience and the size of the automobile involved in the accident.A random sample of its claim files over the past 12 months was selected and claims were categorized according to the size of car (compact,midsize,or large),and also according to the amount of damage (minor,extensive,or write-off).The following table summarizes the results for the sample of 360 claims. The appropriate test in this situation and its degrees of freedom are
A)a t test with 8 degrees of freedom.
B)a test with 1 degree of freedom.
C)a test with 4 degrees of freedom.
D)a z test with infinite degrees of freedom.
E)a test with 8 degrees of freedom.

Question

An insurance company has conducted a study of its accident claim experience and the size of the automobile involved in the accident.A random sample of its claim files over the past 12 months was selected and claims were categorized according to the size of car (compact,midsize,or large),and also according to the amount of damage (minor,extensive,or write-off).The following table summarizes the results for the sample of 360 claims.  The appropriate test in this situation and its degrees of freedom are
A)a t test with 8 degrees of freedom. 
B)a test with 1 degree of freedom. 
C)a test with 4 degrees of freedom. 
D)a z test with infinite degrees of freedom. 
E)a test with 8 degrees of freedom.

Quizplus · Accepted Answer

The appropriate test in this situation is the chi-squared test for independence, which tests whether there is an association between two categorical variables. In this case, the variables are size of car and amount of damage. The degrees of freedom for this test are calculated as (r-1)(c-1), where r is the number of rows and c is the number of columns in the contingency table. In this case, there are 3 rows (compact, midsize, and large) and 3 columns (minor, extensive, and write-off), so the degrees of freedom are (3-1)(3-1) = 4. Therefore, choice C is the correct answer.

An Insurance Company Has Conducted a Study of Its Accident