The doctor knows that people taking the medicine may sleep better just because they expect the medicine to work. how can he be sure of whether the medicine really works?

The best test would be doing a double-blind test between the person who is receiving the medicine so that they don't know if they received a placebo or not and the person giving the medicine does not know if the participant is receiving a placebo or not.

However, a placebo test can simply be done. This is where the patient received a medicine that does not have any medicinal effects and see if the person sleeps better. If they say they did, they have fallen under the placebo effect.

you need to have a picture of the atom that way we can answer it