The __________________________ is the distribution of of the variable x-bar (all possible sample means) for a random variable X and a fixed sample n. Show
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" Recommended textbook solutions
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The Practice of Statistics for the AP Exam6th EditionDaren S. Starnes, Josh Tabor 2,673 solutions What is the standard deviation of the sampling distribution of the sample means?The standard deviation of the sampling distribution of means equals the standard deviation of the population divided by the square root of the sample size. The standard deviation of the sampling distribution is called the “standard error of the mean.”
Which of the following is the standard deviation of the sampling distribution of the sample mean when the population is finite?2) "the formula for the standard deviation of the sampling distribution of the sample mean, σ/√n, holds approximately if the population is finite and much larger than (say, at least 20 times) the size of the sample".
What is the sampling distribution of the sample means?The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).
What is the variance and standard of the sampling distribution of the sample means?Variance. The variance of the sampling distribution of the mean is computed as follows: That is, the variance of the sampling distribution of the mean is the population variance divided by N, the sample size (the number of scores used to compute a mean).
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What is the standard deviation of the sampling distribution of sample means quizlet?
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