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You calculate the actual sample mean, and from that number, you then estimate the probable mean (or the range) of the population from which that sample was drawn.
N is neither the sample or population mean. The letter N represents the population size while the small case letter n represents sample size. The symbol of sample mean is x̄ ,while the symbol for population mean is µ.
n = sample sizen1 = sample 1 sizen2 = sample 2 size= sample meanμ0 = hypothesized population meanμ1 = population 1 meanμ2 = population 2 meanσ = population standard deviationσ2 = population variance
It means you can take a measure of the variance of the sample and expect that result to be consistent for the entire population, and the sample is a valid representation for/of the population and does not influence that measure of the population.