**Core Concept**
The Chi-square test is a statistical method used to determine whether there is a significant association between two categorical variables. The degree of freedom in a Chi-square test is a critical parameter that determines the number of independent pieces of information available to estimate the population parameters.

**Why the Correct Answer is Right**
The degree of freedom for a Chi-square test is calculated as (r-1) x (c-1), where r is the number of rows and c is the number of columns in the contingency table. In this case, the table is 4 x 5, so the degree of freedom is (4-1) x (5-1) = 3 x 4 = 12. This means that there are 12 independent pieces of information available to estimate the population parameters.

**Why Each Wrong Option is Incorrect**
**Option A:** This is incorrect because the degree of freedom is not simply the number of rows (4) or columns (5), but rather a product of the number of rows and columns minus one.
**Option B:** This is incorrect because the degree of freedom is not the sum of the number of rows and columns (4 + 5 = 9), but rather a product of the number of rows and columns minus one.
**Option C:** This is incorrect because the degree of freedom is not the square of the number of rows and columns (4^2 = 16), but rather a product of the number of rows and columns minus one.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the degree of freedom in a Chi-square test determines the number of independent pieces of information available to estimate the population parameters. A higher degree of freedom generally indicates more reliable results, but it also increases the risk of Type I error.

**Correct Answer:** C. 12