1, Does an outfit really improve a professional swimmer's time? To test this, ten professional swim- mers swam a 100 m race wearing three different outfits: a full-body water repellent suit, water- repellent trunks, and non-water repellent trunks. The table below gives the swimmers' time in seconds. At the 5% significance level, determine if the outfit does indeed make a difference. Also test to determine if the swimmer was a confounding factor. Swimmer 1 3. 4 7 8 10 Full-Body Water Repellent Suit Water-Repellent Trunks 49.80 50.52 49.36 50.02 50.36 49.89 50.31 50.05 50.81 49.73 51.07 53.4752.91 53.0753.11 52.8953.14 53.07 53 52.68 Non-Water 53.66 54.91 54.55 53.85 54.63 55.01 55.39 53.93 55.69 55.21 Repellent Trunks 2. With the increase in online courses, university researchers are interested to learn if there is a difference in the average overall grade for students taking an online statistics course with and without video supplements versus students taking a traditional in-class statistics course. Since it is believed that a student's previous statistical knowledge can affect the outcome, the research- ers blocked the students based on their previous statistical knowledge from taking AP statistics: scored 4 or above on the AP Statistics exam, scored below a 3 on the AP Statistics exam, or did not take AP Statistics. The table below gives the student's overall grades. Treatments Blocks In-Class Course On-line with Video On-line without Videos Scored 4 or Above on the AP Statistics Exam 90 93 89 86 88 90 82 84 85 88 79 83 79 76 78 75 77 81 Scored 3 or Below on the AP 91 89 90 93 95 92 86 87 82 82 89 88 81 83 86 82 79 76 statistics Exam Did not Take 93 89 97 88 92 86 86 88 84 87 89 85 78 76 80 77 75 79 AP Statistics a. Test whether the average overall scores differ for the three different types of statistic courses. b. Is there a benefit to blocking on the student's previous statistical knowledge? Justify your answer.