Question

For a fixed alpha level of significance, how is the

critical value for a chi-square test related to degrees of
freedom?
a. The critical value increases as df increases.
b. The critical value decreases as df increases.
c. The critical value increases as sample size increases.
d. The critical value decreases as sample size increases.

Answer 1

The correct answer is A.

For a fixed alpha level of significance, the critical value for a chi-square test is directly related to the degrees of freedom (df). As the degrees of freedom increase, the critical value also increases. This is because as the degrees of freedom increase, the chi-square distribution becomes less skewed and more symmetrical, resulting in a larger critical value needed to reject the null hypothesis.

Sample size, on the other hand, does not have a direct impact on the critical value for a chi-square test. However, larger sample sizes can result in higher degrees of freedom, which would in turn affect the critical value.

Answer 2

The answer is A: the critical value increases as df increases.