AP®︎ Statistics (pre-2026): Topic 5.8 Flashcards

Master key terms and definitions for Topic 5.8 of AP Statistics (pre-2026) – Sampling Distributions for Differences in Sample Means to help you prep for quizzes and the AP exam.

This course has been archived. The College Board updated AP Statistics for the 2026–27 school year, and the units and topics changed.
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Term

Sampling Distribution of x̄1 - x̄2

Definition

The distribution of possible differences between two sample means from repeated random samples.

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Sampling Distribution of x̄1 - x̄2
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The distribution of possible differences between two sample means from repeated random samples.

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Mean and Standard Deviation of x̄1 - x̄2
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Mean is μ1 - μ2; standard deviation is √(σ1²/n1 + σ2²/n2) for independent samples.

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Independent Random Samples
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Samples chosen so one sample's outcomes do not affect the other's outcomes.

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Sampling With Replacement vs. Without Replacement for x̄1 - x̄2
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With replacement uses the usual formula; without replacement gives a slightly smaller standard deviation.

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10% Condition for Differences in Sample Means
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If each sample is under 10% of its population, ignoring reduced spread without replacement is acceptable.

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Interpreting Parameters and Probabilities for x̄1 - x̄2
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State center, spread, or probability in context, with correct units, for the two populations.

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Normality Conditions for x̄1 - x̄2
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It is normal if populations are normal, or approximately normal when both samples are at least 30.

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