ABSTRACT
This chapter explores the extremes of certain probability distributions, principally the Normal Distribution and those that are 'normalesque' like the Student's t-Distribution. Statistical Tests usually involve either Significance Testing or Hypothesis Testing, where the practitioner, estimator, planner etc. tests the validity of an assumption or hypothesis against another. These hypotheses are usually referred to as: the Null Hypothesis and the Alternative Hypothesis. The Standard Error of a sample's statistic is the Standard Deviation of the sample values of that statistic around the true population value of that statistic. It can be approximated by the dividing the Sample Standard Deviation by the square root of the sample size. The Z-Test is one which evaluates whether the value of any Normally Distributed sample statistic is significantly different from a known or assumed value of that statistic for the population overall. Degrees of Freedom are the number of different factors in a system or calculation of a statistic that can vary independently.
