Dear DCstats and ERosa   Starting a new section here because the preceding is hopelessly indented  DCstats and ERosa you are mistaken in your thinking Jdannan and Avenue are quite correct I know this might be very difficult for you to accept You claim to have references supporting your interpretation However I think you are misinterpreting the statements from the textbooks you are reading I cant speak for your petroleum industry statistican friend My guess is that you conveyed your misinterpretation of the situation to himher I have a phd in mathematics and after reading this talk page and thinking I was almost losing my mind I consulted with several other phd mathematician and statistician friends of mine who confirmed that Jdannan and Avenue are indeed correct And the interpretation given in the article is basically correct as well In fact its the interpretation Ive seen given in every stats book Ive looked at  Some references since these seem to be very important to people   Warning There is much confusion about how to interpret a confidence interval A confidence interval is not a probability statement about  since  is a fixed quantity not a random variable  Larry Wasserman All of Statistics A Concise Course in Statistical Inference p  CAUTION A  confidence interval does not mean that there is a  probability that the interval contains  Remember probability describes the likelihood of undetermined events Therefore it does not make sense to talk about the probability that the interval contains  since the population mean is a fixed value Think of it this way Suppose I flip a coin and obtain a head If I ask you to determine the probability that the flip resulted in a head it would not be  because the outcome has already been determined Instead the probability is  or  Confidence intervals work the same way Because  is already determined we do not say that there is a  probability that the interval contains   Michael Sullivan III Statistics Informed Decisions Using Data p  The idea of interval estimation is complicated an example is in order Suppose that for each  x is a real random variable normally distributed about  with unit variance then as is very easy to see with the aid of a table of the normal distribution if Mx is taken to be the interval x   x   then  P in Mx     where  is constant and almost equal to  It is usually thought necessary to warn the novice that such an equation as  does not concern the probability that a random variable  lies in a fixed set Mx Of course  is given and therefore not random in the context at hand and given   is the probability that Mx which is a contraction of x has as its value an interval that contains   Leonard J Savage The Foundations of Statistics p    Your misunderstanding seems to be based on an inadequate grasp of a few facts    The population mean  is a fixed constant not a random variable  The endpoints of the confidence interval are random variables not fixed constants  A statement about the level of confidence of a confidence interval is a probabilistic statement about the endpoints of the interval considered as random variables   The issue about whether  is known or not is a complete red herring What matters is that  is fixed not whether its known This also has absolutely nothing to do with probabilistic interpretations of quantum physics good lord  Let me go through an example which has the most simplifying assumptions Suppose we have a normally distributed random variable X  on a population with mean    and standard deviation    and suppose we select samples of size n   Then the sample mean Xbar is a sampling distribution defined on the space of all possible samples of size  and it has mean    and standard deviation sqrtn  sqrt     A  confidence interval for  based on this sampling is then given by Xbar  zsqrtn Xbar  zsqrtn  Xbar   Xbar    Xbar   Xbar    Now note the following facts    The confidence interval is defined to be a random interval ie the endpoints of the confidence interval are random variables defined in terms of the sample mean Xbar  We know what the population mean  is and yet we wer