Answer: To determine the rejection region of a chi-squared goodness-of-fit or independence test, you need to know the degrees of freedom. Therefore, the correct answer is:
Degrees of freedom.
The degrees of freedom are determined by the number of categories in the data and the number of parameters estimated from the data. The rejection region of the test is based on the chi-squared distribution with degrees of freedom equal to the number of categories minus the number of parameters estimated. The average number of observations per cell, sample size, probability of Type II error, and whether or not to assume the population standard deviations are equal are important factors in determining the power and precision of the test, but they are not directly related to the determination of the rejection region.