Final answer:
To select the appropriate Degrees of Freedom, one must know the type of statistical test being performed. For a Test of Independence, df equals (number of columns - 1)(number of rows - 1), and for a goodness-of-fit test, it's (number of categories - 1). The statement about df equating to sample size minus one is false for a Test of Independence.
Step-by-step explanation:
When choosing the appropriate number of Degrees of Freedom (df) for a test, it depends on the type of statistical test you are conducting. For instance, a Test of Independence calculates df as (number of columns - 1)(number of rows - 1). As for the goodness-of-fit test, df is determined by the formula (number of categories - 1). When we look at the given chi-square table, we need to know either the number of categories or the structure of the contingency table to choose the correct df value. Both the tests for independence and goodness-of-fit tend to use right-tailed critical values.
To ensure the correctness of the test, especially for a goodness-of-fit, the expected value for each cell must be at least five. The statement 'The number of degrees of freedom for a test of independence is equal to the sample size minus one' is false, it's a common mistake to confuse this with df for one-variable tests. When you have the necessary information, you could choose any of the methods mentioned here because you have the necessary information.