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Unit 5: Sampling Distributions

8 dot points across 8 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What makes a statistic an unbiased estimator, and how do bias and variability differ?

Topic 5.4 Biased and Unbiased Point Estimates: define an unbiased estimator (its sampling distribution centers on the parameter), and distinguish the bias of an estimator from its variability.
A focused answer to AP Statistics Topic 5.4, defining unbiased estimators whose sampling distributions center on the parameter, distinguishing bias from variability, and why both matter when choosing an estimator, with a worked comparison.
9 min answer →

Why do different random samples from the same population give different statistics?

Topic 5.1 Introducing Statistics: Why Is My Sample Not Like Yours? Recognize sampling variability, the difference between a parameter and a statistic, and that a statistic varies from sample to sample in a predictable way.
A focused answer to AP Statistics Topic 5.1, on sampling variability, the parameter-versus-statistic distinction, and why a statistic varies predictably from sample to sample, motivating the idea of a sampling distribution.
9 min answer →

How is the sampling distribution of the difference between two sample means described?

Topic 5.8 Sampling Distributions for Differences in Sample Means: describe the mean, standard deviation, and shape of the sampling distribution of the difference between two independent sample means, adding variances and checking the conditions for normality.
A focused answer to AP Statistics Topic 5.8, on the mean, standard deviation, and approximately normal shape of the difference between two independent sample means, the add-the-variances rule, the conditions, and finding probabilities, with full worked calculations.
10 min answer →

How is the sampling distribution of the difference between two sample proportions described?

Topic 5.6 Sampling Distributions for Differences in Sample Proportions: describe the mean, standard deviation, and shape of the sampling distribution of the difference between two independent sample proportions, and check the conditions for the normal model.
A focused answer to AP Statistics Topic 5.6, on the mean, standard deviation, and approximately normal shape of the difference between two independent sample proportions, the conditions, and finding probabilities, with full worked calculations.
10 min answer →

What are the center, spread, and shape of the sampling distribution of a sample mean?

Topic 5.7 Sampling Distributions for Sample Means: describe the mean, standard deviation, and shape of the sampling distribution of a sample mean, using the central limit theorem and the standard deviation formula sigma over root n.
A focused answer to AP Statistics Topic 5.7, on the mean, standard deviation, and shape of the sampling distribution of a sample mean, the sigma-over-root-n formula, the conditions for normality, and finding probabilities, with full worked calculations.
10 min answer →

What are the center, spread, and shape of the sampling distribution of a sample proportion?

Topic 5.5 Sampling Distributions for Sample Proportions: describe the mean, standard deviation, and shape of the sampling distribution of a sample proportion, and check the conditions (10% and large counts) for the normal model.
A focused answer to AP Statistics Topic 5.5, on the mean, standard deviation, and approximately normal shape of the sampling distribution of a sample proportion, the 10% and large-counts conditions, and finding probabilities, with full worked calculations.
10 min answer →

Why is the sampling distribution of the sample mean approximately normal even when the population is not?

Topic 5.3 The Central Limit Theorem: state and apply the central limit theorem, that the sampling distribution of the sample mean becomes approximately normal as the sample size grows, regardless of the population's shape.
A focused answer to AP Statistics Topic 5.3, on the central limit theorem, why the sample mean's distribution becomes normal as n grows regardless of population shape, the large-sample guideline, and its role in inference, with a worked application.
9 min answer →

How does the normal model from Unit 1 carry over to describing sampling distributions?

Topic 5.2 The Normal Distribution, Revisited: revisit the normal model and z-scores in the context of distributions of statistics, finding proportions and using the standard normal as the basis for later inference.
A focused answer to AP Statistics Topic 5.2, revisiting the normal model and z-scores for distributions of statistics, finding proportions and percentiles, and setting up the standard normal as the engine of sampling-distribution calculations.
9 min answer →