X = Parent Population; n = size of sample, M = mean of population, Sigma = st dev of population, S = st dev of sample, Y = sample means. А, и като пиша X ~ Normal имам в предвид "the distribution of X is normal".

1. X ~ Normal, Sigma = known => (Y-M)/(Sigma/Sqrt(n)) ~ N(0,1) for all n.

2. X ~ Normal, Sigma = unknown => (Y-M)/(S/Sqrt(n)) ~ Student t for all n. If n is large, then (Y-M)/(S/Sqrt(n)) -> N(0,1) (because Student t is approximately Normal for large sample sizes n).

3. X ~ Unknown, Sigma = known => (Y-M)/(Sigma/Sqrt(n)) -> N(0,1) for large n (Central Limit Theorem)

4. X ~ Unknown, Sigma = unknown => (Y-M)/(S/Sqrt(n)) -> N(0,1) for large n

така, ся ако някой e запознат би ли обяснил по-подробно как от 3 следва 4.

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