Sampling Distributions - Means

Front

What is a sampling distribution?

Back

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

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What is the Central Limit Theorem?

Back

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

Front

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

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

Front

What is the standard deviation of a sampling distribution called?

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The standard deviation of a sampling distribution is called the standard error.

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How do you calculate the standard error?

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

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What is the relationship between sample size and standard error?

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As the sample size increases, the standard error decreases, leading to a more precise estimate of the population mean.

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What does it mean for a distribution to be normal?

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A normal distribution is a symmetric, bell-shaped distribution where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

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What is the probability of a sample mean falling within a certain range?

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To find the probability of a sample mean falling within a certain range, you can use the Z-score formula and standard normal distribution tables.

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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 Z = (X - μ) / σ.

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What is the significance of the 68-95-99.7 rule?

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The 68-95-99.7 rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.