The __________________________ is the distribution of of the variable x-bar (all possible sample means) for a random variable X and a fixed sample n.
1. If the distribution of X is normal, the distribution of x-bar will be normal too.
2.The Central Limit Theorem (CLT) for a "relatively large" sample size ( n ≥ 30), the variable x-bar is normally distributed regardless of the distribution of the variable. This result gets more accurate as n increases.
3. For samples of any size, the mean of the variable x-bar is the same as the mean of the variable X, that is μx = μ
4. For the samples of any size, the standard deviation of the variable x-bar is the standard deviation the variable X divided the the square root of the size of the repeated samples n, that is σx-bar = σ ÷√n
5. Since σx-bar represents the error/variation from estimating μ with x-bar, it's often called the "standard error of the mean"
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