Correct interpretation of a defect-rate interval

Question

A 95% confidence interval for the true defect rate of a process is $[0.02,\ 0.06]$ . Consider four statements:

(A) 95% of production units have a defect rate between 2% and 6%.
(B) The probability that this particular interval contains the true rate is 0.95.
(C) The method used produces intervals that capture the true defect rate about 95% of the time.
(D) There is a 5% chance the true rate equals exactly 0.04.

Which statement is the correct frequentist interpretation?

Accepted Answer

Answer: (C). Why the others fail. - (A) is nonsense: an individual unit either is or is not defective; it does not have its own defect rate. The interval is about the single process-wide rate. - (B) attaches a probability to one realized interval. Once computed, the interval either contains the fixed true rate or it does not; the 0.95 belongs to the procedure, not this instance. - (D) invents a probability for a specific parameter value. The true rate is a fixed number, not something with a 5% chance of equaling 0.04. Why (C) is right. It correctly frames 95% as the long-run capture rate of t…

Correct interpretation of a defect-rate interval

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