S5E13 The Confidence Interval's Tale
Quantitude
Interpreting Confidence Intervals and Probabilities
Confidence intervals give a range of values where the population mean is likely to fall. When interpreting a 95% confidence interval, it means that 95 out of 100 such intervals constructed from different samples would contain the population mean, not that there's a 95% chance that a specific interval contains the mean. Once an interval is selected, it either contains the mean or it doesn't, with no probability involved in its containment. This clarifies the difference between confidence intervals and probabilities in a frequentist perspective.
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