Final answer:
The explanatory variable in the study is Vitamin E intake, as it is the condition being tested, and the response variable is Heart function post-surgery, which is the outcome being measured.
Step-by-step explanation:
In the given study about vitamin E and heart bypass surgery, the explanatory variable is Vitamin E, as it is the variable that is being manipulated to test its effects on the outcome. The response variable is Heart function post-surgery, which is the outcome that is being measured to see if there was an effect from the intake of Vitamin E. Thus, the correct identification would be: Explanatory variable: Vitamin E; Response variable: Heart function. In the design of such experiments, treatments are the different levels or types of the explanatory variable that the experimental units receive, and the experimental units themselves are the subjects or items that the treatment is applied to. It is important to ensure that there are no lurking variables that could influence the study's outcome, and random assignment, as well as blinding, are methods used to prevent such issues.