Final answer:
A serious shortcoming of a correlational study is that it cannot determine causation, due to the potential presence of confounding variables and lack of experimental manipulation to control other factors. Hence, option (a) is correct.
Step-by-step explanation:
A serious shortcoming of a correlational study is that it cannot determine causation. While a correlational study can tell us the strength and direction of the relationship between two variables, it does not confirm whether one variable causes the other to occur. This limitation is because there could be confounding variables at play, which are not controlled in a correlational study.
Thus, an observed relationship between two variables might be due to some other factor, and without an experimental design that manipulates one variable (the independent variable) while controlling others, it is not possible to establish a causal link.