Next section: The precise meaning of the p value

So, the finding that the maximum difference that can be expected (based on a 99% confidence interval) is itself a very small difference would allow the experimenter to conclude that the drug is not effective. The claim would not be that it is totally ineffective, but, at most, its effectiveness is very limited.

See also: pages 2-3 of "Confidence intervals & hypothesis testing"

Next section: The precise meaning of the p value