The confidence intervals which are calculated for measuring the treatment effect also show the range n which lays the true treatment effect.
We calculate the p-values in order to assess that whether the results of the trials have occurred simply because of chance (it is assumed that there is no real difference between the new and the old treatment and that the study is well conducted) https://www.expertsmind.com/statistics/power-and-confidence-interval-homework-assignment-help.aspx