PROBABILITY AT STATS: (PLEASE ANSWER IN FULL DETAIL AND EXPLANATIONS)

To test two methods of instruction, 50 students are selected at random from each of two groups. At the end of the instruction period, each student is assigned a grade (A, B, C, D, or F) by an evaluating team. The data are recorded as follows: F Grade B D 13 16 11 9 19 16 A 7 4 GROUPI GROUP II 3 Totals 50 50 2 (i) Derive a significance level-a = 0.05 critical region for testing the following complemen- tary hypothesese: Ho: The two groups have the same distribution, Hi :not Ho. (You may use Pearson's theorem.) (ii) Discuss whether the critical region you obtained above gives type I error exactly or ap- proximately 0.05. If you think it is the former, justify; Otherwise, state possible as- sumptions that would make the approximation more accurate. (iii) Execute your hypothesis testing for the data given above. State your conclusion and also a non-statistical interpretation