In discussing a confidence interval estimate for a population mean, is it acceptable to provide an interpretation like the following: "There is a 95 percent chance that ? lies in the range 20 to 40"?
What will be an ideal response?
No, this interpretation is not correct. As stated, it implies that ? is a random variable that can take on different values when in fact ? is a parameter and has a fixed value. The 95 percent confidence level indicates that of all possible confidence intervals constructed from a given size sample selected from the population, and using a z critical value associated with 95 percent confidence, 95 percent of the intervals would contain the true population mean. The particular interval that we actually have computed (20 to 40 ) will either contain ? or it won't.
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