"Empirical evidence"? What does that mean? I have been born again 50 years and I can testify to countless answered prayers. I've found that either people believe me or they don't. I'm not a lab rat for some self appointed expert to observe. Neither do I have to prove anything to anybody. I have a personal relationship with my God in heaven and Jesus is my Lord and Saviour. It makes zero difference to me whether anyone believes me or not. I know the truth. That's good enough for me. Not good enough for anyone else? Tough.
Alright, just one of countless answers to prayer. I was seriously ill with a potentially fatal illness, pancreatitis to be exact. I was so sick I could scarcely pray. My Christian friend came to visit me every day. One day, the doctor came while she was there. My friend prayed, out loud, that my condition would revert to normal. I'd witnessed to the doctor, an Asian woman, previously. She was from a Christian home but not a believer. I was prepped for an operation but they kept putting it off. After 5 days they decided to let me eat again and on the 8th day I went home. The doctor, unprompted, told me that she saw my friend's prayer answered word for word.
Doubt and unbelief are a great blight and curse, and the worst sin that anyone can commit. By saying that God does not answer prayer, you are calling Him a liar. Satan is behind all this. The sooner God's people believe what He says and reject Satan's lies the better.