The core principle governing confidence interval validity is that inference relies on sampling distributions rather than population distributions, requiring either a sufficiently large sample size (n ≥ 30) to invoke the Central Limit Theorem or a normally distributed population for accuracy when samples are small. These conditions necessitate an unbiased random sampling process where the population volume exceeds ten times the sample size to ensure independence among draws and prevent statistical saturation within finite populations. This theoretical framework defines the necessary assumptions for constructing valid parametric inferences regarding interval estimation, distinguishing between negligible bias effects due to non-representative selection and acceptable deviations from normality under asymptotic conditions.
The core principle governing confidence interval validity is that inference relies on sampling distributions rather than population distributions, requiring either a sufficiently large sample size (n…