Many statistical inferential procedures such as hypothesis testing and the estimation of confidence intervals are based on the assumption that the distribution of a sample statistic is normal. The Central Limit Theorem (CLT) often justifies the assumption that the distribution of a sample statistic (e.g., mean, sum score, and test statistic) is normal. The Central Limit Theorem states that, for a large sample of n observations from a population with a finite mean and variance, the sampling distribution of the sum or mean of samples of size n is approximately normal.
- sampling distribution
- normal distribution