1. Students in an introductory statistics course were asked at the begin- ning of the course and at the end of the course the extent to which they disagreed or agreed with the statement: " Statistics is important to my major area of study." They responded on a scale of 1 to 5 with (1) strongly disagree, (2) moderately disagree, (3) neutral, (4) moder- ately agree, and (5) strongly agree. Data are shown in the table. Use a paired-comparison permutation test to determine whether responses to this question changed significantly from the begining to the end of the semester. Student 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 Before 2 3 4 4 3 1 3 4 45 3 4 2 2 4 3 4 2 2 After 2 4 4 4 4 4 3 5 4 4 4 5 2 5 5 41 2 2. 2. Obtain the permutation distribution of the signed-rank statistic SR+ for the following data: Pair 1 2 3 4 Teatment 1 100 250 50 80 Treatment 2 112 240 58 82 3. The data in the table are dry matter contents (in kilogram) of hay ob- tained from experimental plot. The experiment was designed as a ran- domized complete block, and the treatments are three cutting dates Blocks Date 1 2 3 4 5 6Sept.1 1.5 2.1 1.9 2.8 1.4 1.8 Sept. 15 1.8 2.0 2.0 2.7 1.6 2.3 Sep. 30 1.9 2.5 2.5 2.6 2.1 2.4