There is no guarantee that every confidence interval taken from a population will include the population mean.

Question

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Confidence intervals are constructed with a certain confidence level (e.g., 95%), meaning there is a specified probability (e.g., 95%) that the interval will contain the population mean. However, this also implies there is a chance (e.g., 5%) that any given confidence interval might not include the population mean.

There Is No Guarantee That Every Confidence Interval Taken from a Population