In a blind study, the purpose is to reduce bias that may influence responses or outcomes. In data-driven decision making, a blind study is designed so that subjects and response gatherers do not know which treatment is administered, while the researchers do retain this information to correctly manage and analyze the experiment.

In this scenario, dog owners and response gatherers should not know whether the dogs received the medication or a placebo, as this knowledge could influence reporting of outcomes or observations. However, researchers must know which treatment each dog receives to ensure proper administration, monitoring, and statistical analysis.

If neither researchers nor participants knew the assignments, the study would be classified as a double-blind study, which is not stated here. Allowing owners or response gatherers to know treatment assignments would introduce bias and undermine experimental validity.

Therefore, in a blind study, only the researchers should know which dogs received the medication or placebo, making option C the correct answer.