(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)