The True Probability of a Confidence Interval

Area 01 – Scienze matematiche e informatiche

The calculation of a confidence interval, which together with the hypothesis testing is the best known procedure of inferential statistics, has as result the probability that a certain statistical parameter is contained in a certain part of the real line. However this result is not unanimous, because it is widely believed the not be strictly a probability. To this is added the perplexity of being able to replace the said probability with many other equally reliable. In this work these uncertainties are tackled by distinguishing, among all those of the same event, only one probability true and therefore not merely conventional, and then choosing, as result of the determination of a confidence interval, the true inherent probability which, although it is not exactly calculable, however is unlimitedly approximable. This treatment of the confidence interval is then specified for the two cases, of great importance in the experimental sciences, when the statistical parameter is the mean or variance of a normal random variable.

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