It is called "faith", dianaiad, not "evidence".
Prayer is nothing more than belief and faith. Acceptance of prayers that works, is just faith that you believe God has or will answer your prayer.
If prayers were evidences, then even non-believers should be to verify the prayers are true.
Prayer is the evidence of faith. It is NOT the evidence of the truth of that faith.
Faith is...the willingness to behave as if the things you believe to be true are true. "Faith" is trust...and actually has absolutely nothing to do with whether the thing one has faith in is true, factual, or not.
Even if people like to conflate the concepts of 'belief,' and 'faith,' they are not the same thing. After all, even the Bible separates the concepts of faith, belief, and knowledge. It does, after all, mention that 'even the devils believe, and tremble..." but they don't DO anything about that belief, do they?
Here is where I generally pull out the story about my sister, who has plenty of objective evidence that a bridge will hold her up if she wants to cross it. More than most...her husband was a specialist in metal fatigue for NASA, and did a bunch of research on any bridges she might need to cross.
Doesn't matter, though. She will not cross a bridge. Period. ANY bridge that puts her more than two or three feet above the surface, and she gets antsy about those. She has no faith in them. She DOES have faith in ferries and airplanes. For some reason, if it's an overpass that does NOT cross water, she'll go on those, but bridges over water? Not a chance.
So we have two examples, one literary, one real world, about how faith works.
Faith is based upon belief, and every belief is based upon evidence. That evidence may not rise to the level YOU like in objectivity or repeatability, but it is evidence just the same. When I pray, I get what I honestly believe to be an answer, and my beliefs are based upon that answer. I don't really give a hoot whether you approve of that answer as 'proper evidence' or not. It's evidence to ME, and it is evidence to others when they get their own.
To come back to the topic, sort of, I was noting that the reason most people believe what they do, about pretty much everything (including science) is because people they trust tell them that this thing or that thing is 'true.' YOU claim to have taken courses, or done studying on your own about scientific stuff, like the make up of atoms and what they would 'look like' if we could actually take a picture and enlarge it enough to see them.
But...have YOU ever sat down to an electron microscope and looked for yourself? Have YOU ever climbed a volcano and personally dipped a rod into the lava...then examined it yourself? Have YOU repeated the experiments and the logical thought paths that confirmed the scientific theories you accept as true?
My guess is...no. You haven't. Not for most of 'em, anyway.
I'm sure you believe that Mt. Everest is 29,029 feet tall. So do I. It has been measured many times, more and more exactly, until the latest findings, done with modern technology, put it at 29,092 feet.
But did YOU measure it?
Then how did you come to believe that it was that tall?
Because people you trust told you it is, that's how.
It IS possible for you to do your own measuring, true enough, as expensive and dicey a thing to do as that is. That isn't the point. You haven't. And that means that your belief regarding the height of Mt Everest is based PRECISELY on the same thing that my belief in God the Father is; someone you trust told you so.
The difference here is that even though you don't like the evidence that I get when I pray, I at least 'do the experiment." And you can do it yourself without having to fund an international exploratory movement involving Sherpas, climbing gear and satellites.
Now. Do I dismiss all science because I am aware of this? No. Because I DO trust those who tell me stuff; I have reason to do so.
But I am quite aware of the FACT that most of what I understand of the world, scientific or cultural or religious, comes to me through tradition, and through people I trust.
And I don't automatically dismiss evidence because I don't personally approve of it.