3. For a comparison of the academic effectiveness of two junior high schools A and B, an experiment was designed using ten sets of identical twins, where each twin had just completed the sixth grade. In each case, the twins in the same set had obtained their previous schooling in the same classrooms at each grade level. One child was selected at random from each set and assigned to school A. The other was sent to school B. Near the end of the ninth grade, an achievement test was given to each child in the experiment. The results are shown in the accompanying table. Twin Pair A B 67 39 80 75 65 69 70 55 86 74 50 52 63 56 81 72 9 86 89 10 60 47 (a) Using the sign test, test the hypothesis that the two schools are the same in academic effectiveness, as measured by scores on the achievement test, against the alternative that the schools are not equally effective. What would you conclude with a = .05? (b) Suppose it is suspected that junior high school A has a superior faculty and better learning facilities. Test the hypothesis of equal academic effectiveness against the alternative that school A is superior. What is the p-value associated with this test? (c) Repeat the test in (a), using the Wilcoxon signed-rank test. Compare your answers