Apropos of ouyr impending exam in statistics, I submit for your attention the following article.
To me it says two things:
1) It tells you exactly what confidence intervals mean, and what they don’t mean, in plain words.
2) It shows you that the philosophical debates about what probability means are not finished yet.
It took till the nineteen thirties for philosophers to begin to sort out the meaning of the scientific method and experimentation, and it sconnection to probability and statistics. The whole idea that a probability is somehow the same as performing countless identical experiments in parallel universes (so the exact starting state can be identical) is the issue, and once this thought experiment was postulated, we went frorward. It was not till the 1950’s (1957 to be exact) when william Feller wrote his monumental “Introduction to the Theory of Probability” which finally brought this esoteric field down to the level of college students. (I was a student of Feller years later at Princeton, but not in probability; I studied real analysis).
And there are still folks who put forth an alternate view (Bayesians) of the interpretation. So we can say that probability and statistics are still an esoteric realm, capable of many misinterpretations by both experienced practitioners and by neophytes.
Enjoy the article, and if you are in my statistics class, see how it tells you precsely the meaning of a confidence interval!
Supply Chain and Logistics 