The two hypotheses in hypothesis testing are the null and alternative hypothesis. How do you tell which is which? The null is the one that is assumed true throughout the entire test. In this example, it is that the defendant is innocent. The alternative hypothesis is the one for which the claimant would like to pursue evidence. Here, it is that the defendant is guilty.
Each individual juror has their own alpha level. What is an alpha level? As long as you are completely unbiased, and believe the defendant to be innocent before the trial begins, your alpha level would be the point at which enough evidence has stacked up for you to reject this belief.
Here is the counter-intuitive part. When evidence for the alternative keeps stacking up, the probability that your original assumption (the null hypothesis) still holds becomes smaller and smaller. Once that probability falls below your alpha level, you reject the assumption in favor of the alternative. This probability is what statisticians refer to as a p-value. So, a very small p-value is synonymous with a large amount of evidence against the original assumption. This is the most difficult concept for an undergraduate statistics student to comprehend.
This is how science works. We observe things happening in nature. Then we try and explain them and make a hypothesis against some status quo. Then we make more observations. The evidence then continues to build or it doesn't.
This is what has happened with evolution. The evidence has stacked up in such a tremendous fashion, that one would have to have an extremely low alpha level to not accept it. And that is just it. We have a culture that has set the Ultimate Hypothesis Test into the minds of most Americans at a young age. This Ultimate Hypothesis test is as follows.
Null Hypothesis: God created man
Alternative Hypothesis: Man has come about naturally through evolution
That is, 1 x 10^(-99). I just typed it out for emphasis.
So, even though these Americans have been confronted by VAST amounts of evidence (so much in fact, that even the theory of gravity doesn't have near as much), it still isn't enough to make the probability that God created man smaller than the alpha I gave you. Maybe it is just 1 x 10^(-69). Not enough. Null hypothesis maintained.
This is what we are competing against. It is a combination of stubbornness to the 99th degree and an incomprehensible amount of ignorance.
This is the world we live in.
Well, at least there are mind altering drugs to which we can turn.