The following table shows the distribution of employees in an organization.Martha Foreman,an analyst,wants to see if race has a bearing on the position a person holds with this company. For the chi-square test for independence,the degrees of freedom used are _____.
A) 2
B) 16
C) 9
D) 8

Question

The following table shows the distribution of employees in an organization.Martha Foreman,an analyst,wants to see if race has a bearing on the position a person holds with this company.  For the chi-square test for independence,the degrees of freedom used are _____.
A) 2 
B) 16 
C) 9 
D) 8

Quizplus · Accepted Answer

To calculate the degrees of freedom for the chi-square test for independence formula, you need to use the following formula: 
degrees of freedom = (number of rows - 1) x (number of columns - 1)

In this case, there are 4 rows and 3 columns, so the degrees of freedom would be: 
degrees of freedom = (4-1) x (3-1) = 3 x 2 = 6

However, since we are testing for race affecting job position, we have to divide the degrees of freedom by one less than the number of levels for the categorical variable we are testing for independence. In this case, we are testing for independence between race (which has 2 levels - white and non-white) and job position (which has 3 levels - upper management, management, and hourly positions). So, degrees of freedom = (2-1) x (3-1) = 2.

Therefore, the correct answer is C) 9.

The Following Table Shows the Distribution of Employees in an Organization.Martha