The study design that can determine a cause-and-effect relationship is:
Option #2: an experimental study.
Experimental studies, particularly randomized controlled trials, allow researchers to manipulate one or more variables and observe the effects of that manipulation on an outcome. This design helps establish causality because it controls for confounding factors and allows for direct assessment of the impact of the intervention or treatment.
Observational studies (Option #1) and surveys (Option #3) typically identify associations or correlations between variables but cannot definitively establish causation due to potential confounding variables and lack of manipulation.