Miscellaneous Sampling Distributions

Front

What is a sampling distribution?

Back

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 does it mean for a sample mean to be unbiased?

Back

A sample mean is unbiased if its expected value equals the population mean, meaning that on average, it accurately estimates the population parameter.

Front

What is the Central Limit Theorem?

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The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

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How does sample size affect the variability of the sample mean?

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Larger sample sizes result in less variability of the sample mean, leading to more accurate estimates of the population mean.

Tags

CCSS.6.SP.A.2

Front

What is the formula for the standard error of the mean?

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The standard error of the mean (SEM) is calculated as SEM = σ/√n, where σ is the population standard deviation and n is the sample size.

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What is the significance of the standard deviation in a sampling distribution?

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The standard deviation of a sampling distribution, known as the standard error, indicates how much the sample means are expected to vary from the population mean.

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What is a point estimate?

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A point estimate is a single value given as an estimate of a population parameter, such as the sample mean used to estimate the population mean.

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What is the difference between a sample and a population?

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A population includes all members of a specified group, while a sample is a subset of the population selected for analysis.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

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What is a biased estimator?

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A biased estimator is one that does not accurately reflect the population parameter, leading to systematic errors in estimation.

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What is the role of random sampling in statistics?

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Random sampling ensures that every member of the population has an equal chance of being selected, which helps to reduce bias and improve the validity of results.

Tags

CCSS.HSS.IC.B.3