I understand the concept of the NULL hypothesis and how to reject it, however I would like to be able to explain why this is a better approach than trying to prove the alternative hypothesis true.
What would it entail do to "prove" the alternative hypothesis true? I put "prove" in quotations to exempliy that we cannot prove it with certainty, but perhaps we can assign some type of probability of it being true, similar to how we assign a probability of a result given that the NULL hypothesis is true. Can you create a completely fictitous example (for example where the hypothesis space is limited to 3 discrete values), which shows how you would try to prove the alternative hypothesis true? And why would this approach be worse than the NULL approach? Is it because we can only show something is true, by showing that every other possibility is false?