Sampling Distributions

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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 sample mean) obtained from a large number of samples drawn from a specific population.

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What is the Central Limit Theorem?

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The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the population's distribution, if the sample size is sufficiently large (usually n > 30).

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What is the formula for the standard deviation of a sampling distribution?

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

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Define the term 'population' in statistics.

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A population is the entire group of individuals or instances about whom we hope to learn.

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CCSS.HSS.IC.A.1

CCSS.7.SP.A.1

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Define the term 'sample' in statistics.

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A sample is a subset of the population selected for observation and analysis.

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CCSS.HSS.IC.A.1

CCSS.7.SP.A.1

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What is the difference between a population parameter and a sample statistic?

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A population parameter is a value that describes a characteristic of the entire population, while a sample statistic is a value that describes a characteristic of a sample.

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CCSS.HSS.IC.B.3

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What does it mean if a distribution is normally distributed?

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A normally distributed distribution is symmetric about the mean, with most of the observations clustering around the central peak and probabilities for values further away from the mean tapering off equally in both directions.

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What is the significance of the mean in a sampling distribution?

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

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CCSS.6.SP.A.2

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How do you calculate the probability of a sample mean being less than a certain value?

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To calculate this probability, you can use the Z-score formula: 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.

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CCSS.HSS.ID.A.4

Front

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 Z = (X - μ) / σ.