EricPH,
If you have never experienced an answered prayer; then you cannot understand the profound effect you are left with. My numerous experiences can only convince me that God answers prayers. When prayers are answered, I am left with the feeling I have to do something, I have to give something back.
I have, and to be honest I felt a sense of gratitude and awe. But I did not instantly accept that it was a case of Providence. I could have been lucky, or maybe my own efforts led to the outcome/blessing. I do not rule out the possibility that he could have answered my prayer, but I do not believe that is the case with certainty. I am open-minded toward the circumstance.
You seem to believe that you will never be affected by an answered prayer, and your beliefs will probably be proved true. By their very nature, answered prayers are a tricky phenomena to gather evidence for. That is; unless you have a personal encounter.
I don’t, maybe I will who knows, anything is possible. My reasoning is that God is purported to be a personal being. He wants people to have faith in Jesus, therefore he will not allow his existence to be proved in a way that negates that. If he shows he is real, it will be in a personal way to someone. One of the ways he can do that is by answering prayers. As you say, it is difficult to gather evidence for prayers, unless it is so obvious that God has intervened that there is no other conclusion.
Theists believe, agnostics ponder and atheists analyse. A little bit of each should get us the right answer.