\fChi-Square Goodness of Fit Test (Assuming Equal Expected) Items Roll a 1 Roll a 2 Roll a 3 Roll a 4 Roll a 5 Roll a 6 Observed Expected 13 20.00 33 20.00 14 20.00 7 20.00 36 20.00 17 20.00 - Chi Square 2.45 8.45 1.80 8.45 12.80 0.45 - Data Level of Significance Degrees of Freedom 0.01 5 Results Critical Value 15.0863 Chi-Square Test Statistic 34.40 0.0000 p-Value Reject the null hypothesis This tests the null hypothesis that the distribution is equal across all categories. It also tests if there is a difference in the frequencies of the categories / items. Rejecting the null implies a difference in the categories / items. Chi-Square Goodness of Fit Test (Assuming Unequal Expected) Items Sunday Monday Tuesday Wednesday Thursday Friday Saturday Observed % Expected Expected 165 40.00% 160.00 79 20.00% 80.00 50 14.00% 56.00 44 10.00% 40.00 32 8.00% 32.00 20 6.00% 24.00 10 2.00% 8.00 - Chi Square 0.16 0.01 0.64 0.40 0.67 0.50 - Data Level of Significance Degrees of Freedom 0.05 6 Results Critical Value 12.5916 Chi-Square Test Statistic 2.38 0.8818 p-Value Do not reject the null hypothesis This tests the null hypothesis that the distribution is as expected. In other words, it tests if the results fit the expected distribution. Rejecting the null implies that the results do not fit the distribution