The probability distribution of a sample statistic that is formed when random samples of size n are repeatedly taken from a population
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Sampling Distribution of Sample Means
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a distribution obtained by using the means computed from random samples taken from a population
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Properties of Sampling Distribution of Sample Means
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1) the mean of the sample means is equal to the population mean
2) the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size
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Standard Error of the Mean
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the standard deviation of the sampling distribution of the sample means
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Central Limit Theorem forms the foundation for the ___ branch of statistics
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inferential
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The Central Limit Theorem describes the relationship between the ___ of sample means and the ___ that the samples are taken from
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sampling distribution; population
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The Central Limit Theorem is an important tool that provides the information you will need to use ___ to make ___ about a population mean
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sample statistics; inferences
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The Central Limit Theorem
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1) if random samples of size n, where n is greater than or equal to 30, are drawn from any population with a mean and a standard deviation, then the sampling distribution of sample means approximates a normal distribution. The greater the sample size, the better the approximation.
2) if random samples of size n are drawn from a population that is normally distributed, then the sampling distribution of sample means is normally distributed for any sample size n
in either case, the sampling distribution of sample means has a mean equal to the population mean
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Mean of the sample means formula
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mu
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The Central Limit Theorem can also be used to investigate unusual events. An unusual event is one that occurs with a probability of less than ___%
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5
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(T/F) As the size of a sample​ increases, the mean of the distribution of sample means increases.
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false, as the size of a sample​ increases, the mean of the distribution of sample means does not change.
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(T/F) If the size of a sample is at least​ 30, then you can use​ z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.
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this statement is true.
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(T/F) A sampling distribution is normal only if the population is normal.
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the statement is false. A sampling distribution is normal if either n ≥ 30 or the population is normal.
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A population has a mean μ=71 and a standard deviation σ=20. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=249.
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mean = 71
standard deviation = 1.267
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A population has a mean μ=135 and a standard deviation σ=28. Find the mean and standard deviation of the sampling distribution of sample means with sample size n=57.
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mean = 135
standard deviation = 3.709
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