Rarely or ever is the entire population questioned (if the population is small than you will come close sometimes). A sample (often over 1000) is the common practice.
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This is called a sample statistic. They are often used to give a general picture of a more specific whole.
Here are some commonly used symbols in statistics.μ is used to denote the population mean and σ is used for the population standard deviation. Some other very common and important ones arex (with a bar on top) which is used for the sample mean and s which is used for sample standard deviation.
Non-probability or Judgement Samples has to do with a basic researcher assumptions about the nature of the population, the researcher assumes that any sample would be representative to the population,the results of this type of samples can not be generalized to the population(cause it may not be representative as the research assumed) and the results may be biased. Probability or Random samples is a sample that to be drawn from the population such that each element in the population has a chance to be in the selected sample the results of the random samples can be used in Statistical inference purposes
t-test for means
The F distribution is used to test whether two population variances are the same. The sampled populations must follow the normal distribution. Therefore, as the sample size increases, the F distribution approaches the normal distribution.