AP®︎ Statistics (pre-2026): Topic 9.5 Flashcards

Master key terms and definitions for Topic 9.5 of AP Statistics (pre-2026) – Carrying Out a Test for the Slope of a Regression Model to help you prep for quizzes and the AP exam.

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Term

Test Statistic for the Slope of a Regression Model

Definition

Compute t = (b - β0) / SEb to compare the sample slope to the hypothesized slope.

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Test Statistic for the Slope of a Regression Model
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Compute t = (b - β0) / SEb to compare the sample slope to the hypothesized slope.

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Null Distribution for the Slope
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Assuming conditions hold and H0 is true, the standardized slope statistic follows a t-distribution.

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Degrees of Freedom for a Slope Test
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For simple linear regression, use df = n - 2 for the t-distribution of the slope statistic.

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Decision Rule Using P-Value and Significance Level
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Reject H0 if p-value ≤ α; otherwise, fail to reject H0.

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Conclusion About the Population Slope
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State whether there is convincing evidence that the true population slope differs from the null value.

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Null and Alternative Hypotheses for a Slope Test
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State H0: β = β0 and Ha: β < β0, β > β0, or β ≠ β0.

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One-Tailed vs. Two-Tailed Slope Tests
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Use β < β0 or β > β0 for directional claims, and β ≠ β0 for any difference.

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P-Value for a Slope Test
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It is the probability, assuming β equals the null value, of results this extreme.

DAT-3.MDAT-3.M.1
Degrees of Freedom Exception for Slope Test
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When testing a single regression parameter, the slope test uses n minus 1 degrees of freedom.

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