Abstract

How to interpret and make use of a computed (realised) confidence interval has been debated for a long time. I advocate that a realised  confidence interval covers the parameter with probability . Suppose a sample of batteries in routine use is taken and their lifetimes are measured. A confidence interval is computed to  days. The standard interpretation is that if we repeatedly draw samples of the same size and compute confidence intervals, 95% of the intervals will cover the unknown true life time. What can be said about the realised interval  has not been clear in the literature. I shall give contradictory examples of interpretations. To appreciate the claim made here, we need to have a look at philosophy of probability and the Fisherian concept of relevant subsets.