Sampling Distribution

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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 or sample proportion) 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, as long as the sample size is sufficiently large (usually n ≥ 30).

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What is the standard error of the mean?

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

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How does sample size affect the sampling distribution?

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As the sample size increases, the sampling distribution becomes narrower and more concentrated around the population mean, leading to a smaller standard error.

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What is the difference between a population and a sample?

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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.

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CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

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What is a point estimate?

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

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CCSS.HSS.IC.B.3

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What is a confidence interval?

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A confidence interval is a range of values, derived from a sample, that is likely to contain the population parameter with a specified level of confidence (e.g., 95% confidence interval).

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CCSS.HSS.IC.B.4

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What does it mean if a sampling distribution is approximately symmetric?

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If a sampling distribution is approximately symmetric, it means that the distribution of sample statistics is evenly distributed around the mean, resembling a normal distribution.

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

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The mean of a sampling distribution (the expected value) is equal to the population mean, indicating that sample means are unbiased estimators of the population mean.

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What is a null hypothesis?

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A null hypothesis is a statement that there is no effect or no difference, and it serves as the starting point for statistical testing.