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So despite my personal beliefs, with the prevalence of such notions about prayer and God I guess it makes all the sense in the world that people would do a study about it.

Yes, but all the study has shown (to believers) is that God has chosen to behave as He did in that particular occasion, for reasons humans cannot fathom, by definition.

Perhaps He did this just to fool us (the same motivation that guided Him when he buried all those fossils)