Final answer:
An experiment is the most appropriate research method to test the cause-effect relationship between sleep deprivation and anxiety, as it allows for the manipulation of the independent variable and the measurement of the dependent variable.
Step-by-step explanation:
Dr. Jenkins is interested in testing a cause-effect relationship between sleep deprivation and anxiety. To properly assess this relationship, an experiment would be the most appropriate research method (D). This allows for the manipulation of the independent variable, sleep deprivation, and the measurement of the dependent variable, which is the level of anxiety. An example of such an experiment could involve comparing the anxiety levels of participants who are subjected to sleep deprivation with those of a control group that receives normal sleep, ensuring that participants are randomly assigned to conditions.
Correlational studies, case studies, and naturalistic observations are valuable research methods but do not provide the same level of control over variables needed to establish a causal relationship. They can help in identifying patterns or in-depth information pertaining to individual cases but cannot definitively establish that one variable causes changes in another.