Suppose a survey was given to 100 people (the response is just a number between 0 and 1) and only the mean was reported. So 1 sample was taken with n = 100.

Now suppose this was repeated 20 times. So I have a list of means with 20 entries. It's my understanding that I can estimate the population mean and variance by the mean and variance of this list. (Right?)

Given that the # of total people available to survey is infinite, but that the maximum # of times we are allowed to take a survey is 200, my questions are:

Do we calculate standard error as: $SE = \frac{\sigma}{\sqrt{n}}$, where n = 100 or n = 20? Do I use the sample size, or number of samples as $n$?

How does the SE change when increasing sample size vs number of samples... for example what would be the difference of surveying 150 people 20 times vs. surveying 100 people 30 times? (Keeping in mind we only know the mean of each survey)


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