Question

The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides. He takes a sample of recent admissions decisions and forms the following table:



Admitted

Wait List

Denied

Total

Urban

45

21

17

83

Rural

33

13

24

70

Suburban

34

12

39

85

Total

112

46

80

238


He will use this table to do a chi-square test of independence with a level of significance of 0.01. The test will involve ________ degrees of freedom.


12


4


9


6

Answer 1

To find the degrees of freedom for a chi-square test of independence, we can use the following formula:

\[
\text{Degrees of freedom} = (r - 1)(c - 1)
\]

where \( r \) is the number of rows in the contingency table (categories of one variable) and \( c \) is the number of columns (categories of the other variable).

In your case:

- The types of community (Urban, Rural, Suburban) give us 3 rows.
- The admissions status (Admitted, Wait List, Denied) gives us 3 columns.

Now we can calculate the degrees of freedom:

\[
\text{Degrees of freedom} = (3 - 1)(3 - 1) = 2 \times 2 = 4
\]

Thus, the test will involve **4 degrees of freedom**.

Therefore, the correct answer is **4**.