8. (12 points) An article reported the results of a peer tutoring program to help mildly men- tally retarded children learn to read. Suppose that in the experiment, a reading test was administered to both an experimental group and a control group aer 6 weeks of instruction, during which the experimental group received peer tutoring and the control group did not. For the experimental group m = 30 children, the average score on the vocabulary portion of the test was 5:1 = 368.4, with sample standard deviation s1 = 41.0. For the control group $12 = 30 children, 5:2 = 351.0 and 32 = 53.8. Use a signicance level 0.05 to test the claim that the experimental group performed better than the control group. (a) (2 pts) State the null and alternate hypotheses. (b) (2 pts) What test will you use? What assumptions are you making? (c) (4 pts) Calculate the test statistic? (Round to two decimal places.) (d) (2 pts) You may use without calculation that the degree of freedom is 54.1886 3 54. Find the P-value (or the critical value for the rejection region from the t-table if you don't have a scientic calculator). (Round to four decimal places.) (e) (2 pts) State your decision and reason. Interpret your conclusion in the context of the