If l is not too small and H₀ is true F_r has approximately a chi-squared distribution with df = k - 1. The null hypothesis is rejected if F_r chi-square critical value for the given level of significance α.

Question

If l is not too small and H₀ is true F_r has approximately a chi-squared distribution with df = k - 1. The null hypothesis is rejected if F_r > chi-square critical value for the given level of significance α.

Quizplus · Accepted Answer

This statement is true according to the chi-square test for independence. If the null hypothesis is true (i.e. no association between two variables), then the test statistic has a chi-square distribution with degrees of freedom equal to (number of rows - 1) times (number of columns - 1). The critical value of chi-square depends on the chosen level of significance α and the degrees of freedom. If the calculated test statistic is greater than the critical value, then the null hypothesis is rejected in favor of the alternative hypothesis (i.e. there is evidence of a significant association between the variables).

If L Is Not Too Small and H0 Is True

If L Is Not Too Small and H₀ Is True