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 happens to the shape of the sampling distribution as the sample size increases?

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As the sample size increases, the shape of the sampling distribution approaches a normal distribution, regardless of the shape of the population distribution (Central Limit Theorem).

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What is the Central Limit Theorem?

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

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

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The mean of the sampling distribution of sample means (μ_x-bar) is equal to the mean of the population (μ).

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What is the standard deviation of the sampling distribution of sample means?

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The standard deviation of the sampling distribution of sample means (σ_x-bar) is equal to the population standard deviation (σ) divided by the square root of the sample size (n): σ_x-bar = σ/√n.

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If a population is strongly right-skewed, what can be said about the sampling distribution for a sample size of 49?

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For a sample size of 49, the sampling distribution will be approximately normal due to the Central Limit Theorem.

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What is the probability of obtaining a sample proportion?

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The probability of obtaining a sample proportion can be calculated using the normal approximation to the binomial distribution when the sample size is large enough.

Tags

CCSS.HSS.ID.A.4

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How do you calculate the z-score for a sample mean?

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The z-score for a sample mean can be calculated using the formula: z = (x̄ - μ) / (σ/√n), where x̄ is the sample mean, μ is the population mean, and σ is the population standard deviation.

Tags

CCSS.HSS.ID.A.4

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What is the significance of a sample size of 30 in statistics?

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A sample size of 30 is often considered the minimum size for the Central Limit Theorem to hold, allowing the sampling distribution of the mean to be approximately normal.

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What does it mean if a sampling distribution is not normal?

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If a sampling distribution is not normal, it may indicate that the sample size is too small or that the population distribution is not suitable for normal approximation.