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.