(a) Why is the Normal distributionso important, particularly with respect to problems dealing with statistical inference?
(b) Ok, now that we accept/believe that the Normal distribution is so widely applicable, computationally why is it so useful?
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(a) Why is the Normal distribution so important, particularly with respect to problems dealing with statistical inference?
The ultimate goal of most statistical inference tests is to evaluate relations between variables. Let us assume that we have already calculated a measure of a relation between two variables. The next question is “how significant is this relation?” For example, is 40% of the explained variance between the two variables enough to consider the relation significant? In order to determine the level of statistical significance, we need a function that represents the relationship between “magnitude” and “significance” of relations between two variables, depending on the sample size. The function we need would tell us exactly “how likely it is to obtain a relation of a given magnitude (or larger) from a sample of a given size, assuming that there is no such relation between those variables in the population.” In other words, that function would give us the significance (p) level, and it would tell us the probability of error involved in rejecting the idea that the relation in question does not exist in the population. This “alternative” hypothesis (that there is no relation in the population) is usually called the null hypothesis. In most cases we know its shape and can use it to determine the significance …
Normal distribution is clearly depicted in this solution.