Is p value telling the truth?

Consider a series of experimental testing in drug efficiency, denoted by D1,D2, ...,D20.Suppose now we have two hypotheses:H0 : Drug is not efficient. H1 : Drug is efficient.if cut-off point is preset as 0.05, suppose one of the test results is a p.value=0.045, andanother is p.value=0.016, we statistically reject H0, drawing conclusion that both drugsare efficient. As mentioned above, we need to do 20 tests under the same hypothesisstructure. Then, basically, we can obtain 20 p values, suppose all the p values can belisted below:
Table 1 Drug TestingDrug
D1 D2 D3 D4 D5 D6 D7 D8 D9 D10
p value 0.41 0.31 0.049 0.045 0.016 0.21 0.30 0.209 0.102 0.122
Drug D11 D12 D13 D14 D15 D16 D17 D18 D19 D20
p value 0.121 0.003 0.091 0.40 0.273 0.192 0.167 0.311 0.28 0.22
But the problem is how strong is the evidence that the non-efficient drug istruly coming from non-efficient group?
For more details, see my report, require it ? just send email to stefanie.cao@gmail.com with title "require for p value report".