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The z-distribution is normal distribution. It is the most important of all because there is a theory called the central limit theorem that states that the average of any random variables is approximately normally distributed if the average is over very large number. The t-distribution is when the sample size is small when using it for the average of random variables. The chi-square distribution and F-distribution are used very similar occasion where the test statistics are positive values such as standard error or variances. When the test is something about them, those two distributions are used....
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