Practice question · Multiple choice
The Central Limit Theorem says the distribution of sample means approaches normality as n grows, regardless of the population's shape. Why is 'regardless of the population's shape' the remarkable part?
Hints
- Ask what you would need to know about a population before doing inference, if the theorem were false.
- The theorem is about the distribution of MEANS. What is it not about?
Show the answer
D. Because normal-based inference then applies to non-normal variables.
Why
Without the theorem, testing a hypothesis would require knowing the population's shape, which is almost never available. It makes that ignorance survivable. Guard against the misreading: individual incomes stay resolutely skewed however large the sample, it is the distribution of sample means that becomes normal, and only for samples drawn randomly.
Practise Sampling and Representativeness
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