Solution
What a 95% Confidence Interval Means
Show the problem again
A researcher computes a 95% confidence interval of [10.2, 14.8] for a population mean. Is it correct to say "there is a 95% probability the true mean lies in [10.2, 14.8]"? Answer yes or no, and know the correct interpretation.
Worked solution
No, the 95% refers to the long-run coverage of the procedure, not this particular interval. In frequentist statistics the true mean is a fixed number; once the interval is computed, it either contains the mean or it doesn't; no probability remains. The correct statement: if the sampling and interval-construction procedure were repeated many times, about 95% of the resulting intervals would contain the true mean. Assigning probability to the parameter itself requires a Bayesian credible interval.
Source: Standard interpretation question following the frequentist definition of Jerzy Neyman (1937). Statement written for AxiomIQ.