Final answer:
The number of Degrees of Freedom for a Test of Independence or a goodness-of-fit test varies based on the test and is used alongside critical value tables at specific significance levels to assess the null hypothesis.
Step-by-step explanation:
To choose the appropriate number of Degrees of Freedom for a test, you need to understand the context of the test and how degrees of freedom are calculated in that context. In a Test of Independence, the degrees of freedom are calculated as the product of the number of rows minus one and the number of columns minus one, which is expressed as (number of columns - 1)(number of rows - 1).
For a goodness-of-fit test, the Degrees of Freedom are equal to the number of categories minus one, denoted as df = (number of categories – 1). In both types of tests, you will then refer to the critical value tables to determine the critical chi-square value that corresponds to your desired level of significance (commonly 0.05 or 0.01) and compare it with your calculated chi-square statistic to make a decision on the null hypothesis.