In a way, it’s strange for religious believers to be so invested in the belief that prayer works. If God is all-knowing, perfectly good, and perfectly wise, why would he need our input on how to run the universe? In spite of that, the belief that prayer works is still very important to many believers.
How important? Important enough that for some believers, astronomer and science-popularizer Carl Sagan (1934-1996) marked himself as the enemy when he said:
We can pray over the cholera victim, or we can give her 500 milligrams of tetracycline every 12 hours. (There is still a religion, Christian Science, that denies the germ theory of disease; if prayer fails, the faithful would rather see their children die than given them antibiotics.) We can try nearly futile psychoanalytic talk therapy on the schizophrenic patient, or we can give him 300 to 500 milligrams a day of clozapine. The scientific treatments are hundreds or thousands of times more effective than the alternatives (The Demon Haunted World, pp. 9-10).

I want to briefly return to the subject of chapter 3. Some people who would like critics of religion to just be quiet are particularly concerned about public statements by scientists, because they worry about how criticisms of religion by scientists will affect the acceptance of science by a religious public. To them, Richard Dawkins is the ultimate disaster for public acceptance of science.

Anyone who thinks that way should pause to consider the above quote. In context, Sagan wasn’t trying to bash religion but to praise science. It comes from a book, The Demon Haunted World, where Sagan also said:

Of course many religions—devoted to reverence, awe, ethics, ritual, community, family, charity, and political and economic justice—are in no way challenged, but rather uplifted, by the findings of science. There is no necessary conflict between science and religion (p. 277).