Sampling Distributions in Statistics

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What is a sampling distribution?

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A sampling distribution is the probability distribution of a statistic (like a mean or 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 if the sample size is sufficiently large (n ≥ 30), regardless of the population's distribution.

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What is the difference between a population and a sample?

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A population is the entire group of individuals or instances about whom we hope to learn, while a sample is a subset of the population selected for analysis.

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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 difference between a one-sample and a two-sample distribution?

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A one-sample distribution compares a sample mean to a known population mean, while a two-sample distribution compares the means of two different samples.

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What is a proportion in statistics?

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A proportion is a statistical measure that represents the fraction of the total that possesses a certain characteristic, often expressed as a percentage.

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What is the difference of proportions?

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The difference of proportions compares the proportions of a characteristic between two different groups or populations.

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What is the significance of a sample size of n ≥ 30?

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A sample size of n ≥ 30 is significant because it allows the sampling distribution of the mean to be approximately normal, according to the Central Limit Theorem.

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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.

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What is the purpose of hypothesis testing?

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Hypothesis testing is a statistical method used to make decisions about the population based on sample data, determining whether to reject or fail to reject a null hypothesis.