A study was designed to measure the effect of home environment on academic achievement of 12-year-old students. Because genetic differences may also contribute to academic achievement, the researcher wanted to control for this factor. Thirty sets of identical twins were identified who had been adopted prior to their first birthday, with one twin paced in a home in which academics were emphasized (Academic) and the other twin placed in a home in which academics were not emphasized (Nonacademic). The final grades (based on 100 points) for the 60 students are given in the attached file. a. Is there a difference in the mean final grades between the students in an academically oriented home environment and those in a non-academically oriented home environment? Use =0.05. b. What test did you use? What evidence do you have that the test's assumptions are valid? c. Estimate the size of the difference in the mean final grades of the students in academic and nonacademic home environments using a 99% confidence interval. d. Does it appear that using twins in this study to control for variation in final scores was effective as compared to taking a random sample of 30 students in both types of home environments? Why or why not? 'SetTwins' 'Academic' 'NonAcademic' 1 78 71 2 75 70 3 68 66 4 92 85 5 55 60 6 74 72 7 65 57 8 80 75 9 98 92 10 52 56 11 67 63 12 55 52 13 49 48 14 66 67 15 75 70 16 90 88 17 89 80 18 73 65 19 61 60 20 76 74 21 81 76 22 89 78 23 82 78 24 70 62 25 68 73 26 74 73 27 85 75 28 97 88 29 95 94 30 78 75