Background: Classical confidence intervals are traditionally formulated within the framework of measure theory, probability spaces, and \ (\) -algebras. In the present work, we introduce a simplified approach to confidence bounds based on lower and upper confidence levels. Material and Methods: The proposed approach avoids explicit dependence on measure-theoretic foundations and instead presents confidence bounds as a relation between repeated observations and admissible parameter regions. In general, we define lower (pL) and upper (pU) confidence bounds\ (pL pU, \) with\ (pU = pL +, \) where\ (\) denotes the confidence width. Results: For events considered certain, \ (p = pU = 1. \) By identifying\ (=, \) where\ ( (0, 1) \) denotes the significance level of the underlying statistical test, representing the maximal tolerated probability of falsely rejecting the null hypothesis, the lower confidence bound becomes\ (pL = 1-. \) The right-tailed p-value for observing (pL) in\ (n\) independent trials becomes\ (p-valueₑ₈₆₇ₓ: = (1-) ⁿ. \) Conclusion: We show that under conditions, where the empirical lower confidence bound is equal to\ (pL = 1-, \) then it is reasonable to accept that the underlying p-value satisfies\ (p-valueₑ₈₆₇ₓ: = (1-) ⁿ. \)
Ilija Barukčić (Sun,) studied this question.