Sampling Distributions and CLT

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What is a sampling distribution?

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A sampling distribution is the probability distribution of a statistic (like the mean or proportion) obtained from a large number of samples drawn from a specific population.

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What is the Central Limit Theorem (CLT)?

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The Central Limit Theorem states that the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, as long as the sample size is sufficiently large (usually n ≥ 30).

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What is the mean of the sampling distribution for sample means?

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The mean of the sampling distribution for sample means is equal to the mean of the population from which the samples are drawn.

Tags

CCSS.6.SP.A.2

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How do you calculate the standard deviation of a sampling distribution (standard error)?

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The standard deviation of a sampling distribution (standard error) is calculated as the population standard deviation divided by the square root of the sample size (σ/√n).

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What is a z-score?

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A z-score indicates how many standard deviations an element is from the mean. It is calculated as (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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What does a z-score of 1.14 indicate?

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A z-score of 1.14 indicates that the value is 1.14 standard deviations above the mean.

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What is the formula for calculating the z-score for sample means?

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The formula for calculating the z-score for sample means is z = (X̄ - μ) / (σ/√n), where X̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Tags

CCSS.HSS.ID.A.4

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What is the mean of the sampling distribution for proportions?

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The mean of the sampling distribution for proportions is equal to the population proportion (p).

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How do you calculate the standard deviation of the sampling distribution for proportions?

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The standard deviation of the sampling distribution for proportions is calculated as √[p(1-p)/n], where p is the population proportion and n is the sample size.

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What does a standard deviation of 0.019 for a sampling distribution indicate?

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A standard deviation of 0.019 indicates the variability of the sample proportions around the population proportion.