Which way is correct to write confidence intervals: [a; b] or (a; b)? In several sources of information, I found contradicting ways, how confidence intervals (CI) are presented. Thus, I am confused and would like to find out which one is correct: either $CI_{95\%} = [14.7,19.9]$, or $CI_{95\%} = (14.7,19.9)$. I.e. are 14.7 and 19.9 included in the interval or excluded?
In my opinion, the right way is to write the answer, which is in square brackets: $CI_{95\%} = [0.7, 1.0]$. But is there a theoretical explanation?
 A: Synthesizing @whuber's answer, and googling a bit:


*

*it seems at least one person writes the interval as $(\cdot, \cdot)$, https://www.mathbootcamps.com/three-ways-write-confidence-interval/

*however this source also uses the $+/- \text{margin-of-error}$ notation

*and at the end they conclude:


*

*if you are taking a statistics course, it is of important to pay attention to how your professor or textbook prefers to present confidence intervals and generally stick to that method

*If instead, you are using confidence intervals in your research, it is probably important to consider your audience. Most people have no trouble understanding the idea of adding and subtracting a margin of error, even if they haven’t had much formal training in statistics



As far as the use for statistical significant testing, @whuber has a huge and comprehensive reply at https://stats.stackexchange.com/a/18259/10278 :
"Yes, there are some simple relationships between confidence interval comparisons and hypothesis tests in a wide range of practical settings. However, in addition to verifying the CI procedures and t-test are appropriate for our data, we must check that the sample sizes are not too different and that the two sets have similar standard deviations. We also should not attempt to derive highly precise p-values from comparing two confidence intervals, but should be glad to develop effective approximations."
A: Because a confidence interval represents a range from a continuous probability distribution, the area under the curve encompassed by the interval is theoretically equal whether or not you include the interval boundaries. (Recall that if X is a continuous random variable, then P(X=x)=0.)  Thus, both forms are mathematically correct, but if a teacher or employer of yours prefers a particular notation I'd recommend using that to avoid unnecessary conflict.
A: If we consider the braces from real analysis point of view then we should use [], means both the end values with the braces are also included. In theoretical sense [] and () is same.
