With only 30 people in the negative control group, the confidence interval on the false positive rate would easily swamp out the results of the study for 1.5% p

With only 30 people in the negative control group, the confidence interval on the false positive rate would easily swamp out the results of the study for 1.5% positive sample ratio, no? Seems kind of useless unless your control group is a lot larger, and the false positive rate can be shown to be <<1.5%.