A distribution of statistics
Fix a population, sampling design and sample size. The sampling distribution records the probabilities of the statistic’s possible values under repeated sampling.
Probability & statistics / English
Sampling Distributions AP Statistics Chapter 7 Lesson 7.1.2
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Define a sampling distribution and illustrate it through repeated sample proportions and a chip experiment.
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0:00A distribution of statistics4:30Exact versus simulated distribution10:30Center and unbiasednessLearning script
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Fix a population, sampling design and sample size. The sampling distribution records the probabilities of the statistic’s possible values under repeated sampling.
A dot plot from repeated samples approximates the sampling distribution. It need not include every possible sample and can vary with the number of simulation repetitions.
Under the specified random-sampling model, the sample proportion is unbiased for the population proportion. The observed mean of 35 estimates is close to 0.5 here; finite simulations need not match the parameter exactly.
Knowledge cards
Exact versus simulated distribution
A dot plot from repeated samples approximates the sampling distribution. It need not include every possible sample and can vary with the number of simulation repetitions.
Center and unbiasedness
Under the specified random-sampling model, the sample proportion is unbiased for the population proportion. The observed mean of 35 estimates is close to 0.5 here; finite simulations need not match the parameter exactly.
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- Sampling ExplanationAt 0:00
Why this connection?
Fix a population, sampling design and sample size. The sampling distribution records the probabilities of the statistic’s possible values under repeated sampling. A dot plot from repeated samples approximates the sampling distribution. It need not include every possible sample and can vary with the number of simulation repetitions. Under the specified random-sampling model, the sample proportion is unbiased for the population proportion. The observed mean of 35 estimates is close to 0.5 here; finite simulations need not match the parameter exactly.
Questions this video answers
Find a method↗
A dot plot from repeated samples approximates the sampling distribution by showing the empirical frequencies of the statistic's values. It need not include every possible sample and can vary with the number of simulation repetitions.
Conditions: Repeated samples are drawn from the population.; A dot plot is constructed from the resulting statistics.
Understand why↗
Yes, under the specified random-sampling model, the sample proportion is unbiased for the population proportion. However, the observed mean of a finite number of estimates need not match the parameter exactly.
Conditions: A specified random-sampling model is used.; The estimator is the sample proportion.; The target parameter is the population proportion.
10:30 – 11:26Watch this moment ↗
Meet the concept↗
A sampling distribution records the probabilities of the statistic’s possible values under repeated sampling, given a fixed population, sampling design, and sample size.
Conditions: The population is fixed.; The sampling design is fixed.; The sample size is fixed.
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