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A bit of explanation might be helpful. This is an economics issue with essentially an infinite number of assets. There is some number of participants, each of whom may randomly choose some small fixed number of assets, say 20, from that infinite number available. So what I would like to say is, for example, each participant has a 95% chance of choosing a set which has a mean of property x in some interval as opposed to saying with 95% confidence that the population mean of property x lies in some interval. So it somehow seems to me that pulling multiple samples of size 20 and testing those would give me a better indication of the distribution of sample means than pulling one large sample. On the other hand that seems dumb and the two methods should be equivalent. Any guidance would be appreciated.