Table A4: 5% Critical Values of the F Distribution Numerator Degrees of Freedom 2 3 5 7 8 9 10 Denominator 10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 Degrees of 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 Freedom 12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 11. What is your conclusion? 12. Using t-test, is there a significant difference between low-ability and high-ability pupils? (two-tailed test, level of significance at 0.05) Degrees Significance level of 20% 10% 5% 2% 1% 0.1% freedom (0.20) (0.10) (0.05) (0.02) (0.01) (0.001) 3.078 6.314 12.706 31.821 63.657 636.619 1.88G 2.920 4.303 G.965 9.925 31.598 1.638 2.353 3.182 4.541 5.841 12.941 1.533 2.132 2.776 3.747 4.604 8.610 1.476 2.015 2.571 3.365 4.032 6.859 1.440 1.943 2.447 3.143 3.707 5.959 1.415 1.895 2.365 2.998 3.499 5.405 1.397 1.860 2.306 2.896 3.355 5.041 1.383 1.833 2.262 2.821 3.250 4.781 10 1.372 1.812 2.228 2.764 3.169 4.587 11 1.363 1.796 2.201 2.718 3.106 4.437 12 1.356 1.782 2.179 2.681 3.055 4.318 13 1.350 1.771 2.160 2.650 3.012 4.221 14 1.345 1.761 2.145 2.624 2.977 4.140 15 1.341 1.753 2.131 2.602 2.947 4.073 16 1.337 1.746 2.120 2.583 2.921 4.015 17 1.333 1.740 2.110 2.567 2.898 3.965 18 1.330 1.734 2.101 2.552 2.878 3.922 19 1.328 1.729 2.093 2.539 2.861 3.883 20 1.325 1.725 2.086 2.528 2.845 3.850I. ONE-WAY ANOVA & T-TEST: A study was conducted to determine the effectiveness of the collaborative method in teaching English among pupils of varying ability levels. The performance of 18 pupils on an English test is presented in table below. Low Ability Pupils Middle Ability Pupils High Ability Pupils 45 55 59 58 42 54 61 41 62 59 48 57 49 36 48 63 44 65 Based on the output, answer the following questions: 1. State the null and alternative hypothesis. 2. What are the means and standard deviations of each group? Low Ability Pupils Middle Ability Pupils High Ability Pupils Mean Standard Deviation 3. What is the BSS? 4. What is the degree of freedom (k-1)? 5. What is the BMS? 6. What is the WSS? 7. What is the degree of freedom (N-1)? 8. What is the WMS? 9. What is the f-ratio? 10. What is the critical value
