The 95% confidence interval is best thought of as the region within which there is a 95% probability that the population mean lies.

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A 95% confidence interval means that if we were to take many samples and build a confidence interval from each of them, we would expect 95% of those intervals to contain the true population mean. It does not imply a 95% probability that the population mean lies within a specific interval calculated from a single sample.

The 95% Confidence Interval Is Best Thought of as the Region