I didn't see this particular survey -- although I've seen other surveys that reached the opposite conclusion. Part of the problem is that not every prayer is genuine, nor is every prayer made in accordance with God's will.
More than once I've visited someone in the hospital whose case had seemed hopeless, but who was now recovering. The only explanation the doctors could give was that God must have intervened, in answer to the prayers of His people. This doesn't mean God will answer every prayer the way we wish He would -- but it does mean we ought to pray in times of difficulty, and we ought to trust God for the outcome. The Bible says, "Pray for each other so that you may be healed. The prayer of a righteous man is powerful and effective" (James 5:16).
Why is prayer possible -- and not only possible, but of great comfort to us? The reason is because God loves us, and He delights in the prayers of His people. If God didn't love us, prayer would be a futile exercise. But He does love us, and He wants us to bring our burdens and cares to Him. The proof is that His Son gave His life for us.
Don't be cynical about prayer -- and most of all, don't be cynical about God. Instead, turn to Him and commit your life to Jesus Christ. It's the most important decision you'll ever make.