AP®︎ Statistics (pre-2026): Topic 7.9 Flashcards

Master key terms and definitions for Topic 7.9 of AP Statistics (pre-2026) – Carrying Out a Test for the Difference of Two Population Means to help you prep for quizzes and the AP exam.

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Term

Two-Sample t-Test for a Difference of Means

Definition

A significance test comparing two population means using sample means and estimated standard errors.

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Two-Sample t-Test for a Difference of Means
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A significance test comparing two population means using sample means and estimated standard errors.

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Two-Sample t-Test Statistic
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(x̄1 - x̄2 - 0) divided by the square root of s1^2/n1 + s2^2/n2.

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Standard Error of the Difference of Two Means
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The estimated spread of x̄1 - x̄2, computed as the square root of s1^2/n1 + s2^2/n2.

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Degrees of Freedom for a Two-Sample t-Test
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A technology-based value between the smaller of n1 - 1 and n2 - 1 and n1 + n2 - 2.

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Null Hypothesis for Two Means
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States that the population means are equal, written as μ1 = μ2 or μ1 - μ2 = 0.

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Alternative Hypothesis for Two Means
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States that the population means differ, or that one population mean is greater or less.

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p-Value in a Two-Sample t-Test
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The probability, assuming equal population means, of getting a result at least as extreme.

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Decision Rule Using α
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Reject H0 when p-value ≤ α; otherwise fail to reject H0.

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Conclusion in Context for a Two-Sample t-Test
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State whether the data give convincing evidence about a difference in population means in context.

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Using Technology for a Two-Sample t-Test
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Calculator or software output provides the test statistic, degrees of freedom, and p-value.

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Significance Level
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The cutoff probability used to decide whether to reject the null hypothesis.

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