I consider “occurred coincidentally”, “is a coincidence”, and “occurred by chance” interchangeable. They are all equivalent to the null hypothesis. If my dice

I consider “occurred coincidentally”, “is a coincidence”, and “occurred by chance” interchangeable. They are all equivalent to the null hypothesis. If my dice are loaded then the two 6’s weren’t a coincidence. They were guaranteed. So to say they happened by coincidence is to say the dice are fair (the null hypothesis is true). Consider a typical English sentence: “was it just a coincidence that I saw Frank in town, or was he following me?” They are two alternative hypotheses to explain the same observation: In the first scenario, we assume that Frank was going about his business and just happened by chance to be in the same place as I. In the second, we assume Frank was following me and that’s why he was in the same place. The question is about the hypothesis invoked to explain the observation. “Coincidence” is a (null) hypothesis.