>One of my wife's principals was convinced the prayer jar she provided for the staff was effective because over half of the prayers the prior year had been answered.
Depending on the prior probability of the prayers that were answered (and those that weren't), 51% could be plenty to support the efficacy of the prayer jar.
I know, the problem is that she was evidently entirely unaware that without knowing something about the probability of "answered prayers" absent the prayer jar, the simple "over half of all wishes came true" was entirely meaningless. Without more information any number could, potentially, support either conclusion (did/did-not work). This wasn't said in jest, either, if you're wondering (I did).
Depending on the prior probability of the prayers that were answered (and those that weren't), 51% could be plenty to support the efficacy of the prayer jar.