It always pissed me off when some JW would say, like it happened to my mom: "Sister. I had a huge headache and I prayed to Jehovah and in an hour it was gone!" What bullshit, I thought to myself. I thought: Is Jehovah that meticulous and manipulating to be paying attention to a stupid headache? Can't these people figure out that the headache would have gone away eventually? I neglected to ask if they had taken an aspirin.
There have been numerous "prayer studies" most of which, in my estimation, show no correlation between the beseeching and desired results, especially those studies where the prayer is from a group of people on behalf of another individual. My best guess why people like to pray for others is due to the clustering illusion. It's a logical fallacy.
In spite of that, I think there's another mechanism when prayer is conducted meditatively for yourself. That is related to the "placebo" effect and has been demonstrated in clinical tests. Doctors have know for years that there is a certain positive mental effect which can make someone heal or go into remission from cancer but defeats someone else who just gives up. Whether that is manifested via prayer, strong belief, meditation, belief in lifestyle changes, etc, is not of much consequence as long as it has the desired mind/body effect.
I just refuse to reply to people or agree with them on FB when they request for prayers. I don't think Jehovah is computer savvy.