I have a question about confidence intervals.
In general, are confidence intervals open or closed?
The short answer is “Yes”.
The longer answer is that it does not really matter that much because the ends of the intervals are random variables based on the sample (and assumptions, etc.) and if we are talking a continuous variable then the probability of getting an exact value (the bound equaling the true parameter) is 0.
Confidence intervals are the range of null values that would not be rejected, so what do you do if you compute a p-value that is exactly α? (another probability 0 event for continuous cases). If you reject when p=α exactly then your CI is open, if you don’t reject then the CI is closed. For practical purposes, it doesn’t matter that much.