7.1 Central limit theorem: assumptions and conditions

Assumptions and conditions

To use the normal model, we must meet some assumptions and conditions. The Central Limit Theorem assumes the following:

Randomization Condition: The data must be sampled randomly. Is one of the good sampling methodologies discussed in the chapter “Sampling and Data” being used?

Independence Assumption : The sample values must be independent of each other. This means that the occurrence of one event has no influence on the next event. Usually, if we know that people or items were selected randomly we can assume that the independence assumption is met.

10% Condition: When the sample is drawn without replacement (usually the case), the sample size, n , should be no more than 10% of the population.

Sample Size Assumption: The sample size must be sufficiently large. Although the Central Limit Theorem tells us that we can use a Normal model to think about the behavior of sample means when the sample size is large enough, it does not tell us how large that should be. If the population is very skewed, you will need a pretty large sample size to use the CLT, however if the population is unimodal and symmetric, even small samples are acceptable. So think about your sample size in terms of what you know about the population and decide whether the sample is large enough. In general a sample size of 30 is considered sufficient if the sample is unimodal (and meets the 10% condition).