ABSTRACT
In some instances, the normal distribution may not be the appropriate distribution for studying research variables and/or the population data may not be normally distributed on which we base our statistics. The normal probability distribution however is still useful because of the Central Limit Theorem. The Central Limit Theorem state that as sample size increases a sampling distribution of a statistic will become normally distributed even if the population data is not normally distributed. The sampling distribution of the mean of any nonnormal population is approximately normal, given the Central Limit Theorem, but a larger sample size might be needed depending upon the extent to which the population deviates from normality. Typically, a smaller sample size can be randomly drawn from a homogeneous population, whereas a larger sample size needs to be randomly drawn from a heterogeneous population, to obtain an unbiased sample estimate of the population parameter. If the population data are normally distributed, then the sampling distribution of the mean is normally distributed; otherwise larger samples of size N are required to approximate a normal sampling distribution. The sampling distribution of the mean is a probability distribution created by the frequency distribution of sample means drawn from a population. The sampling distribution, as a frequency distribution, is used to study the relationship between sample statistics and corresponding population parameters.
