9. For each of the following studies, say which is the explanatory variable and which is the response variable. Also, say whether the study is observational or experimental.a. Forestry researchers wanted to compare the growth rates of trees growing at high alti-tude to that of trees growing at low altitude. They measured growth rates using the space between tree rings in a set of trees harvested from a natural forest.

b. Researchers randomly assign diabetes patients to two groups. In the fi rst group, the patients receive a new drug tasploglutide, whereas patients in the other group receive standard treatment without the new drug. The researchers compared the rate of insulin release in the two groups.

c. Psychologists tested whether the frequency of illegal drug use differs between people suffering from schizophrenia and those not having the disease. They measured drug use in a group of schizophrenia patients and compared it with that in a similar sized group of randomly chosen people. d. Spinner Hansen et al. (2008) studied a species of spider whose females often eat males that are trying to mate with them. The researchers removed a leg from each male spider in one group (to make them weaker and more vulnerable to being eaten) and left the males in another group undamaged. They studied whether survival of males in the two groups differed during courtship.

e. Bowen et al. (2012) studied the effects of advanced communication therapy for patients whose communication skills had been affected by previous strokes. They randomly assigned two therapies to stroke patients. One group received advanced com-munication therapy and the other received only social visits without formal therapy. Both groups otherwise received normal, best-practice care. After six months, the communication ability (as measured by a standardized quantitative test score) was measured on all patients.

10. Each of the examples (a-e) in problem 9 involves estimating or testing an association between two variables. For each of the exam-ples, list the two variables and state whether each is categorical or numerical.