AP®︎ Statistics (pre-2026): Topic 7.6 Flashcards

Master key terms and definitions for Topic 7.6 of AP Statistics (pre-2026) – Confidence Intervals for the Difference of Two Means to help you prep for quizzes and the AP exam.

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Term

Two-Sample T-Interval for a Difference Between Means

Definition

An interval estimate for μ1 - μ2 using x̄1 - x̄2 and a two-sample t procedure.

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Two-Sample T-Interval for a Difference Between Means
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An interval estimate for μ1 - μ2 using x̄1 - x̄2 and a two-sample t procedure.

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Parameter and Point Estimate for Two Means
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Parameter: μ1 - μ2; point estimate: x̄1 - x̄2.

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Sampling Distribution of x̄1 - x̄2
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Has mean μ1 - μ2 and, when conditions hold, is approximately normal.

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Standard Deviation vs. Standard Error for x̄1 - x̄2
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Population SD is √(σ1²/n1 + σ2²/n2); estimated SE is √(s1²/n1 + s2²/n2).

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Margin of Error for a Difference of Means
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Critical value times the standard error: t*√(s1²/n1 + s2²/n2).

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Confidence Interval Formula for μ1 - μ2
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(x̄1 - x̄2) ± t*√(s1²/n1 + s2²/n2).

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Critical Value t* and Degrees of Freedom
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Use the t-distribution critical value for the chosen confidence level with appropriate technology-based degrees of freedom.

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Not Pooled
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Treat the two population variances as unknown and not assumed equal.

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Calculator: 2-Sample T Interval
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Use the two-sample t-interval command to enter sample statistics or data and compute the interval.

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Conditions for a Two-Sample T-Interval
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Use two independent random samples or random assignment, check 10% when sampling, and verify approximate normality.

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Interpretation of a Confidence Interval for μ1 - μ2
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We are C% confident the interval captures the true difference μ1 minus μ2.

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