# Statistics 323-Single Sample Confidence Intervals for Large and Normally Distributed Data.pdf

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Single Sample Confidence Intervals for Large and Normally Distributed Data Interpreting Confidence Intervals Although the derivation of a confidence interval for a parameter technically ends with the following probability statement: ࠵? ࠵? ! ࠵? ࠵? ! = 1 ࠵? it is incorrect to say: The * probability * that the population parameter ࠵? falls between the lower value ࠵? ! and the upper value ࠵? 1 ࠵? . For example, it is incorrect to say "the probability that the population mean is between 27.9 and 30.5 is 0.95." Take a second to think about why this is incorrect… In short, most statisticians don't like to hear people trying to make probability statements about constants, when they should only be making probability statements about random variables. If it's incorrect to make the statement that seems obvious to make based on the above probability statement, what is the correct understanding of confidence intervals ? Here's how statisticians would like the world to think about confidence intervals: (1) Suppose we take a large number of samples, say 50. (2) Then, we calculate a 95% confidence interval for each sample. (3) Then, "95% confident" means that we'd expect 95%, or 47.5, of the 50 intervals to be correct, that is, to contain the actual unknown value μ So, what does this all mean in practice? ! is .