The population is the set of all things which you wish to study. However, because collecting information from a large, possibly infinite, population is likely to be prohibitively large and time consuming, it is collected from only some members of the population. This subset is a sample.
The population may, but need not, consist of people. It could be the set of cars, or plots of land. There are a number of different ways of selecting samples: how the sample is selected will influence the quality of the statistics collected and, therefore, the validity of any conclusions.
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A sample is a subset of the population.
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.