Confidence intervals are itself random variables and computed from the estimates mean $\hat \mu$ and standard deviation $\hat \sigma$ of a sample. The 95%-CI would be $\hat \mu \pm 2\cdot \frac{\hat \sigma}{\sqrt n}$. Let's assume we know the true parameter $\mu$ and $\sigma$ and want to compute the interval $\mu \pm 2\cdot \frac{\sigma}{\sqrt n}$. Is there a name for this kind of interval? In german it is called Mutungsinterval.
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How about (approximate) "acceptance region" or "region of acceptance" (of the two-sided test $H_0$: "true parameter = $\mu$" vs. $H_A$: "true parameter $\not= \mu$" with significance level $\alpha = 5\%$)?
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$\begingroup$ This is not the usual meaning of an acceptance region, which refers to a set of values of a test statistic. Here, the question is about a distributional property. $\endgroup$– whuber ♦Nov 25, 2019 at 17:34
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1$\begingroup$ Let me cite from the original question: "Let's assume we know the true parameter $\mu$ (...)". So the question is about an assumption or hypothesis regarding the parameter, and the assumption is that its true value equals $\mu$. This is exactly the situation of a statistical test. I'm not saying that you can't see that interval or the question itself from some other point of view, but you can definitely see it as about an acceptance region in the context of a statistical test (of which I omitted some details, of course). $\endgroup$– schottiNov 25, 2019 at 17:57