A confidence interval represents our confidence that any given value belongs to the set .
It lets us tackle questions like
- If I give a patient a drug and they get better, how likely was it that they would have got better anyway, i.e. they belong to the set of patients who would have got better anyway.
- If I give 100 oatients a drud, and 50 of them get better, how likely is it that the drug works?