Which reading of a confidence interval is correct?

Question

A 95% confidence interval for a strategy's mean monthly return is $[1.2\%,\ 3.4\%]$ . Consider four statements:

(A) 95% of monthly returns fall between 1.2% and 3.4%.
(B) There is a 95% probability the true mean lies between 1.2% and 3.4%.
(C) If we repeated the sampling many times, about 95% of the intervals built this way would contain the true mean.
(D) We are 95% confident the sample mean is between 1.2% and 3.4%.

Which statement is the correct frequentist interpretation?

Accepted Answer

Answer: (C). Why the others fail. - (A) confuses the interval for the mean with the spread of individual returns. A confidence interval describes the average, not where single observations land. - (B) treats the fixed true mean as random. In the frequentist view the mean is a fixed unknown; it is either in [1.2, 3.4] or not. The 95% is a property of the procedure, not of this one interval. This wording would be right only for a Bayesian credible interval. - (D) is about the sample mean, which we already know exactly (it is the center, 2.3\%). There is no uncertainty to attach a confidence lev…

Which reading of a confidence interval is correct?

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