Earlier quoted context omitted.
I can see the analogy here but a test like that being binary throws things off and that's also super asymmetrical error. Weren't we sampling a gaussian?
It’s the same principle. The “trivial interval” from the first link (the one you called pedantry), which is applicable to a Gaussian and tweakable to have different coverage than 50%, clearly shows that being an n% confidence interval, on its own, doesn’t guarantee the ability to directly translate that n% into post-data inferences. Likewise, in the truncated exponential example, when you compute that confidence inte…
The examples that actually ruin the number so far have been asymmetrical. Is there a way to do it with a gaussian? Especially if you're trying to make a reasonable internal?