Numerous surveys have been done on things such as the efficacy of prayer on cardiac patients and results are frankly so inconclusive as to be meaningless*.
I've seen double blind tests that claim to prove beyond a shadow of a doubt that prayer has no value, but I've also seen others claim to prove that prayer has great value. I've even seen one that showed that those receiving prayer did significantly worse than those who did not!
It is known that those with religion convictions tend to live slightly longer than those without, but since this effect is noted regardless of the faith followed and *all* faiths cannot, by definition, be true only a fool would attempt to claim there is anything supernatural at work here, instead giving a psychological explanation. It may also be that us unbelievers die earlier because we're just more fun.
* although one could argue that this shows there is no attributable effect.