So I am working on a project and the question came up: How far out of the range of a bunch of intervals $ \{ [a_i, b_i] \}^N_{i=1}$, when is it suspicious when $c_i \not \in \{ [a_i, b_i] \}^N_{i=1}$. Because we are trying to perform hypothesis testing on a data set that contains many variables. For the work I am working on this variable is a range that is made up of several other variables.
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"Suspicious" is not a term with a precise mathematical meaning. For a mathematical answer to your question you should [edit] to provide context and a definition. – Ethan Bolker Mar 16 '24 at 21:00
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You question is not clear, please reformulate it or explain it by an example. – trula Mar 16 '24 at 21:00
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Generally speaking, you need a model here. Only in the context of a model can you decide whether some data points are likely or not. And, typically, even if you have a model, you can only decide such a thing up to some confidence level. – lulu Mar 16 '24 at 22:25