Answered prayer vs. random chance or human intervention
The entire problem with answered or unanswered prayers is the vagueness. You can be the sort of person who asserts that every good thing in your life, including your daily meals, is an answered prayer. However, at that point you move into a hazy area where anything, from your father’s work ethic to the happenings of the universe, could be attributed to prayer.
In the world of scientific studies, for finding to have significance, they must rise above the statistical noise. This means that these findings must have a positive percentage above what you would expect from random variation. Unless you go the above mentioned route where ever little thing is a round-about answered prayer, then god never rises above the statistical noise. In other words, 500 people have stage III cancer. The average survival rate is 30%, which means in order for answered prayers of the 500 cancer patients to rise above the statistical noise, god would have to save around 40-50% of them (and even then, that wouldn’t be that impressive). These sort of studies have been done, and god never rises above the noise. So the effects of prayer are either so vague that we can’t notice them, or no more significant than random variation of given events. It’s not that answered prayer isn’t tangible or obvious, it’s never more significant than random chance.
When I look at that, I conclude that it is more likely that god doesn’t exist then that god is meagerly behind mundane everyday events that would occur the same way given random variation with or without a godlike presence. God is either on the sidelines not doing much, or isn’t there at all.