Answer:
A. Observational study
Explanation:
In research, an observational study is a type of study in which the researcher observes a phenomenon and tries to establish some relationship between the different variables he/she is observing. In other words, the researcher only observes and doesn't give a treatment.
On the other hand, when we have a experiment, we usually have 2 different groups (one that will receive a treatment and one who won't) and the researcher compares the differences between these two groups because of the treatment. In other words, the researcher does something other than just observing.
In this example, the research is going to determine if there is a relation between hearing loss and exposure to mumps. In this example the researcher is only going to observe how people who have been exposed to mumps are regarding hearing loss (we can say this since it will be unethical for example for the researcher to create an experiment in which he/she exposes a group to mumps). Therefore, he is going to observe how the past exposure to mumps could be related with the hearing loss.
Thus, this is an observational study.