Does a confidence interval contain a mean if the proposed mean equals one of its limits?
For example, say I have a 95% confidence interval ranging from 3.19 to 3.49. Does this interval contain the mean 3.19?
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If continuous variables are concerned (I guess yours is), it shouldn't really matter, because the probability of the RV being equal to an exact value is actually 0. You should consider the mechanics behind it to understand better. While calculating these intervals, we find some probabilities in the form $P(X \leq u)$ or $P(X<u)$, which are the same. First one produces a closed CI, while the latter produces an open one. If you're that unlucky, i.e. your mean is exactly the same with your limit, you should first consider adding more resolution to your CI or mean calculation. Round it to more decimals than two.