Interpretation of Sampling Distribution and Relationship to Test Statistics Explain what a sampling distribution is and why it is important to understand the sampling distribution of a test statistic.
This is the way that I understand it:
A sampling distribution is the probability distribution of a statistic that comes from a large number of independent samples drawn from a population.  The sampling distribution of a test statistic is important because this allows us to assign a probability to the occurrence of an event that we may be interested in; it allows us to know the likelihood that the collected data tells us something useful.  Without knowing the sampling distribution, this probability can’t be assigned accurately.
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It is often impossible to test every member of a population, but if it were, one can know for certain the characteristics of the population. Since it is not practical to test the entire population it is often the case that a randomly chosen sample, or subset, of the population is analyzed. The sample is ran through tests in hopes of finding relationships in the data which not only reflect the current state of the population via the sample but allow reliable predictions (inferences) of future states. The relation or correlation of frequencies, if one exists, is the sample distribution which models the randomly selected sample in such a way as to accurately represent the population as a whole. This is why the larger the sample, the more accurate the distribution, because the sample is approaching the population size.
