05C - The Hong Kong University of Science & Technology...

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ISMT 111: Business Statistics Tutorial Set 5 Sampling Distribution of Sample Statistics The sampling distribution of a statistic is the probability distribution of all the possible values of this statistic which are computed from random samples with same sample size ( n ) . Notation: n = Sample size X = Random variable µ = Population mean X = Sample mean σ = Population standard deviation s = Sample standard deviation se = Standard error p = Population proportion b p = Sample proportion Central Limit Theorem (CLT) Regardless of the population distribution of X which with a mean µ and a standard deviation σ , i fthesamp les ize n is su ciently large ( n > 30 ), the sampling distribution of the sample mean X will be APPROXIMATELY normally distributed with the mean µ X = µ , and the standard deviation σ X = σ n when n > 30 X CLT N ( µ, σ 2 n ) Note : There are four possible cases: Normal Population Nonnormal Population n is large ( n > 30)
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05C - The Hong Kong University of Science & Technology...

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