(1) What test/design would you use in each of the following contexts? (a) I ask a set of 30 people to climb three different hills one after the other. Each hill has a different incline and different peak point. I want to know whether there is a significant difference in climbing times. What kind of design and test would you use for this? (0.5 Points) (b) A set of 90 patients are randomly assigned to one of the three diet control treatments. I want to see if their cholesterol values have changed significantly after a three-month program. What design and test would your use for this? (0.5 Points) (c) You need to test the effect of drinking green tea and exercise on the weight loss patterns of a set of 100 patients. There are three possible levels (Easy, Medium, Hard) for the exercise and two possible levels for green tea consumption (moderate and heavy). What design and test would your use for this? (0.5 Points) (d) In plain English, explain what are main and interaction effects in part (c)? (0.5 Points) (2) A firm is trying to decide which website to use from a set of websites. The web developer provided six designs in total. There were two factors involved in the design. The first one was with whether there was social media integration in the design or not. The second one was how many sections the website had (4, 5 or 6). Given below is the data on the time that users spent (in seconds) on each of the different designs.

	Number of Sections
4	5	6
Social Media	121 111 102 103 104 127 122 124 119 118	93 95 90 90 87 77 121 135 123 91	104 103 101 152 153 152 156 177 164 172
No Social Media	67 68 64 62 69 69 74 75 72 75	88 86 87 89 92 93 94 96 93 91	108 107 106 105 104 103 102 111 119 101

(a) What was the effect of having social media integration on the website vs not having it? (0.5 Points) (b) Was there a significant difference between having three, four and five sections on the website? What were the differences like (0.5 Points) (c) Is the interaction effect significant? How is it different from having only one of the two (1 Point) (d) Which design would you recommend? Is it significantly better than other designs? (1 Point)