Spot the false statement about a confidence interval

Question

A 90% confidence interval for a population mean is $[50,\ 58]$ . Consider four statements:

(A) The interval came from a procedure with 90% long-run coverage.
(B) The confidence level describes the procedure, not this specific interval.
(C) Before the sample was drawn, the probability the resulting interval would cover the mean was 0.90.
(D) After computing this interval, there is a 90% probability the mean is in $[50, 58]$ .

Which statement is false?

Accepted Answer

Answer: (D). Why (A), (B), (C) are all correct. Each keeps the 90% attached to the procedure or to the pre-data random interval. Statement (C) is subtle but valid: before sampling, the interval you are about to build is random, so it genuinely has a 0.90 chance of covering the fixed mean. Why (D) is false. Once the interval is computed, it is a fixed set of numbers and the mean is a fixed number. The event "mean is in [50, 58]" is now either true or false; no probability strictly between 0 and 1 applies. This is the single most common confidence-interval error. Takeaway. The probability state…

Spot the false statement about a confidence interval

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