A sample is a subset of the population.
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A random sample is a sample (subset of the population) where each member of the population has an equal chance of being sampled. See related links.
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
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.
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.
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.