3. A sociology student wanted to test to see if the GPA's of four sororities were significantly different. They found the following: Let A = group 1, B = group 2, C = group Sorority A B C D yi 3.22 3.57 2.87 2.98 Si 0.54 0.35 0.21 0.23 ni 10 10 10 10 3, and D = group 4. (a) Calculate SSB. (b) Calculate SSW (c) Calculate d. f{B}. (d) Calculate d. f{W}. (e) Calculate MSB. (f) Calculate MSW (g) Calculate the F test statistic.Continue with Problem 3 (the sorority problem). Assume a = 0.05 (a) State the null and alternative hypothesis mathemat ically. (b) State the null and alternative hypothesis in terms of the problem. (c Calculate the range for the pvalue. (d Interpret the pvalue in terms of the problem. ) ) (e) Do you reject or fail to reject the null hypothesis? (f) Interpret your conclusion in terms of the problem. ) What 95% condence interval between two means will certainly not contain zero if we were to create it? (h) What type of error could we have made in this ques tion? (g (i) Interpret a Type II error in terms of the