241 connecting confidence intervals and hypothesis tests

From a paper by Greg Kochanski:

How are confidence intervals related to Hypothesis Tests?

They are very much equivalent. If the confidence interval doesn’t include H0, then a hypothesis test will reject H0, and vice versa. In fact, if you made up a vast number of different null hypotheses, one after the other, then tested them, the accepted null hypotheses would mark out the confidence interval.

Confidence intervals put the focus on the measured number; hypothesis testing puts the focus on the theory that you are testing.