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Sample Mean Distribution

Sample Mean Distribution - a the population being sampled...

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Sampling Distribution of the Sample Mean x Summary of Characteristics and Properties 1. The mean ( 29 x E The mean of all possible sample means, ( 29 x E , is the mean of the population μ . Symbolically, ( 29 μ = x E 2. The standard deviation x σ a. The standard deviation of all possible sample means, x σ , is directly proportional to the standard deviation of the population σ through the square root of the sample size n . Symbolically, n x σ σ = The standard deviation of all possible sample means, x σ , is given a special name. It is referred to as the standard error of the mean or the standard error of x . b. If the sample size n is not very much smaller than the size N of the population, then the standard error of x is modified to take into account the finiteness of the population . Symbolically, 1 - - = N n N n x σ σ The factor ( 29 ( 29 1 - - N n N is called the finite population correction factor or fpc . © 1999 by Harvey A. Singer 1
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3. Range Probabilities The random variable z ( 29 n
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Unformatted text preview: a. the population being sampled is normal, or b. the population is non-normal but the samples are at least moderately large ( n > 30) Part b is an approximation that follows from the Central Limit Theorem. According to the Central Limit Theorem, the sampling distribution of the sample mean looks more and more normal as the sample size increases beyond n = 30. Decision Paths Standard Error of the Mean Population infinite finite- N-→ ∞- n/N « 1 n x = 1--= N n N n x © 1999 by Harvey A. Singer 2 Probabilities Population normal non-normal n x z σ μ-= sample size n ? (1) large small n ≥ 30 n < 30 n x z-= ? (1, 2) Notes (1) z follows the standard normal distribution. Use s if unknown (unavailable). (2) Approximately normal by Central Limit Theorem. © 1999 by Harvey A. Singer 3...
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