5.4 Chi-Square Test of Goodness of Fit and IndependenceThe X2(chi-square) distribution is used to test (1) if observed frequencies differ“significantly” from expected frequencies when more than two outcomes arepossible; (2) if the sample distribution is binomial, normal, or other; and (3) if twovariables are independent or not.enciesectedfrequfffeeexpfsfrequencieobservedfWhere(5.4)e0202If the calculated X2is greater than the tabular value of X2at the specified level ofsignificance and degrees of freedom (from App.6), the null hypothesis, H0, isrejected in favor of the alternative hypothesis, H