Question

What is the impact that any lack of normality will have on the choice of sampling distribution?

Answer 1

Definition -

A sampling distribution is a probability distribution of a statistic obtained through a large number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.

Following are the impacts -

1) if the sample from sampling distirution is not following normal distribution then there may be chance that we have to go for non parametric tests for testing of the hypothesis about the population and statistic

2) In order to compute to the probabilities of some events if the data is normally distributed then it becomes easy for computation perspective by considering normal distribution.

3) The avaiblibility  of the various parametric tests also becomes uneasy if the underlying sampling distribution is not normal