Final answer:
The key criterion for making a causal inference about the relationship between two variables is the ability to randomly assign study participants to groups. The correct answer is option C.
Step-by-step explanation:
The key criterion for making a causal inference about the relationship between two variables is C) The ability to randomly assign study participants to groups.
In order to establish causality, it is important to eliminate any lurking variables that can cloud the study. Random assignment of participants to treatment groups ensures that all potential lurking variables are spread equally among the groups, and the only difference between the groups is the treatment imposed by the researcher. This allows for a cause-and-effect connection to be proven between the explanatory and response variables.