AP®︎ Statistics: Topic 2.12 Flashcards

Master key terms and definitions for Topic 2.12 of AP Statistics – Sampling Distributions and the Central Limit Theorem to help you prep for quizzes and the AP exam.

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Term

Sampling Distribution

Definition

Distribution of a statistic’s values for all possible samples of a fixed size from a given population using the same random sampling process

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Sampling Distribution
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Distribution of a statistic’s values for all possible samples of a fixed size from a given population using the same random sampling process

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Sampling Variability
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Sample-to-sample variation in a statistic when different random samples are selected

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Population Distribution vs Sample Distribution vs Sampling Distribution
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Population distribution: values of a variable for the whole population; sample distribution: values in one sample; sampling distribution: values of a statistic across all possible same-size samples

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Simulated Sampling Distribution
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Approximation of a sampling distribution made by repeatedly taking random samples from a population or model, calculating the statistic, and recording it

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Steps To Simulate a Sampling Distribution
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Specify population/model and parameter values, choose fixed n, generate a random sample, calculate the statistic, record it, repeat many times, and graph the recorded statistics

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Sample Size vs Number Of Repetitions
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Sample size is the number of observations in each sample; repetitions are the number of simulated statistics used to approximate the distribution

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Randomization Distribution
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Distribution of a statistic generated by repeatedly randomly reallocating or reassigning observed response values to treatment groups and recalculating the statistic

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Sampling Distribution vs Randomization Distribution
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Sampling distribution comes from repeatedly drawing new random samples from a population or model; randomization distribution comes from repeatedly reassigning existing response values to treatment labels

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Central Limit Theorem
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For the mean x̄ of a random sample, the sampling distribution can be approximated by a normal distribution; the larger the sample size, the better the approximation

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What The Central Limit Theorem Applies To
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The theorem applies to the sampling distribution of the sample mean x̄, not to the population distribution or the data in one sample

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Effect Of Larger Sample Size On The Sampling Distribution Of x̄
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As n increases, the sampling distribution of x̄ becomes less spread out; if the population is not normal, it also becomes more nearly symmetric and bell-shaped

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Law Of Large Numbers vs Central Limit Theorem
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Law of large numbers: a long-run average gets closer to its expected value; central limit theorem: the sampling distribution of sample means becomes approximately normal as n increases

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Random Sample
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Sample selected by a random process so the observations can be treated as representative draws from the population model

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