I cannot speak for anyone but myself regarding that. I have had prayers answered completely and beyond a shadow of a doubt, because of the way in which they were prayed for, and how they were answered. I have seen friends and family members have their prayers answered, some completely, others in a round-about way. There have been "Gideon" prayers made, with only certain requests made, and only those requests answered. But like I said, I can only speak from my own personal experience with prayer.
There have also been a couple of things that have happened in my young adult and now in my middle-aged life. Things that I heard and knew exactly what it was; something I smelled that was not there, but represented something about someone, at the time (that was also involved with answer to prayer.)
There were 3 certain things that happened with my older son when he was much younger - that would send shivers down your spine - or at least it did with myself, my husband, and some friends who saw or heard. One thing had to do with seeing our daughter's guardian angel hovering overhead - his eyes, our other son's eyes, and our daughter's eyes were all watching whatever it was at the ceiling. He could not understand why daddy and mommy could not see her angel watching over her.
Another was something he saw happen in the sky or heaven (as he called it) and could not understand why I could not see Jesus looking out of the little door in the sky. I humored him at first trying to look and see a cloud shaped door or whatever, but he said the door had closed and I had missed out.
The 3rd thing had something to do with "sensing" 16 pregnancies in a row (of myself, our pastor's wife at the time, a couple of other ladies in the church, and outside of the church (friends)) - and how he knew what God had picked them to be, whether boy or girl. The 16th one, and the last one, I might add, he "sensed," took place when he was 6 years old. Our close friends had been trying to conceive for years and could not. He upped and said one day to her that they were going to have a baby boy on a Tuesday. After him getting 15 others right, this was by far the oddest because she wasn't pregnant then, and why the Tuesday?
A few months later, the friend's cousin had a baby at the age of 15, and didn't want it. The aunt/uncle discussed with our friends whether or not they would like to adopt the baby, and they said they would, plus that would keep it in the family, so to speak. About 3 months after the baby was born, they went to the different state to finalize the adoption. The baby was a boy, by the way.
A few days later, she called, all excited because they officially now had their baby boy, and it was also on a Tuesday! We all had shivers then. Our son just looked at us and said, "I told ya so that that's what God wanted for them - baby boy on Tuesday."
Anyway, those things that happened were in our personal lives, and while we saw, heard, or experienced things, that were definitely out of the ordinary, I realize it doesn't meant it will be accepted by you or anyone else, and that's fine. We experienced them, others did who were around us during that time, and that's what counts for us.
Our pastor at the time, while in Israel, had an experience that happened, that totally stunned him, and while some didn't believe him, others did. When he started sharing about it, including offering some studies regarding what he learned over there, he became quite ill from some infection acquired overseas, and died - no one, not even his wife, ever really knew just exactly what had happened while in Israel, but it changed him greatly.
I am not in the habit of sharing things like this on a forum board, but went ahead tonight, anyway. All I ask, please, that if you choose to disregard any and all of it, that is perfectly fine, but please don't make an issue of it, or laugh about it, or mock it - only because they are special to me and my family, and we did experience it, ourselves. I still don't feel I should explain totally what happened with my personal experiences that I mentioned, mainly because they are very personal and mean a lot to me.
Thank you for indulging me with the length - I'm sorry it is rather long.