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I'm slightly confused why the 95UCL (upper confidence limit) is of the population mean (as typically stated in most explanations) and not of the sample mean.

For example, if from of a population of unknown mean and standard deviation a number of items are selected to provide a single data set then the calculation of the 95UCL is based solely on the statistics of that data set (eg the sample mean) and nothing to do with the statistics of the population (which are unknown).

If more items are selected from the population then the data set is larger and the sample mean provides a more accurate calculation of the population mean. However, the population statistics have not changed - what has changed is the statistics of the data set - they have becoming more accurate to the population statistics. Surely, then it is the UCL of the sample mean that has changed, not the UCL of the population mean (which is a constant, but unknown, value).

Thanks in advance. If this is incorrect please can you provide an explanation why it is the UCL of the population that is calculated and not the UCL of the sample mean.

Regards, Mat

M. Rouge
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  • You are confusing a margin of error with a confidence interval. A confidence interval is a set of plausible hypotheses in the parameter space, for which the observed result is within a $100(1-\alpha)\%$ margin of error. [Here](https://stats.stackexchange.com/a/554340/307000) is a related thread on margin of error. [Here](https://stats.stackexchange.com/a/552522/307000) is a related thread on visualizing a confidence interval for a Bernoulli proportion. – Geoffrey Johnson Dec 22 '21 at 19:24

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1) Confidence interval is calculated for unknown quantities. There is uncertainty around (estimate of) population mean, not sample mean. So, UCL of population mean is calculated not sample mean.

2) 95% Confidence interval explanation : When confidence intervals are calculated from all possible samples (of same sample size n), then actual population mean will belong to 95% of those CIs.

Yes, CI changes whenever your sample changes. But, a larger sample size normally will lead to a better estimate of the population parameter.

sree22
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    Thanks for the above. i agree with points 2 and 3, which i already knew, but I don't agree with your answer for point 1. There is no uncertainty around the population mean (it's just that its value is unknown); there is uncertainty about the estimate of the population mean which in itself is represented by the sample mean plus a margin of error. – M. Rouge Sep 30 '17 at 19:54