A 95% confidence interval is sometimes expressed as stating that when drawing many samples, 5% of the times the mean will lie within a confidence interval.

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A 95% confidence interval means that out of many intervals constructed from different samples, we can expect 95% of them to contain the true population mean. It does not mean that the true mean will be within the interval 95% of the time.

A 95% Confidence Interval Is Sometimes Expressed as Stating That