AP®︎ Statistics (pre-2026): Topic 7.5 Flashcards

Master key terms and definitions for Topic 7.5 of AP Statistics (pre-2026) – Carrying Out a Test for a Population Mean 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This course has been archived.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

One-Sample T-Test for a Population Mean

Definition

A significance test for whether a population mean differs from a hypothesized value using sample data.

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One-Sample T-Test for a Population Mean
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A significance test for whether a population mean differs from a hypothesized value using sample data.

DAT-3.F
Matched Pairs T-Test
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A t-test on the mean of pairwise differences from two related measurements on the same subjects.

VAR-7.E
T-Test Statistic for a Mean
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t = (x̄ - μ0)/(s/√n), comparing the sample mean to the null mean in standard-error units.

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Test Statistic for Matched Pairs
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t = (d̄ - μd0)/(sd/√n), using the sample mean and standard deviation of differences.

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Standard Error of the Mean
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s/√n, the estimated standard deviation of the sampling distribution of the sample mean.

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Degrees of Freedom for a One-Sample T-Test
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n - 1 for a single sample or for the number of matched-pair differences.

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Sampling Distribution of the T Statistic
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When sampling from a normal population, the statistic follows a t-distribution with n - 1 degrees of freedom.

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One-Tailed vs. Two-Tailed Test
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Use one tail for directional alternatives and two tails for non-directional alternatives.

DAT-3.E
Conclusion of a Mean T-Test in Context
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State whether the data give convincing evidence for the alternative claim about the population mean.

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Using a T-Table to Estimate P-Value
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Match the test statistic with df = n - 1 and read the tail probability; double it for two-sided tests.

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Calculator Output for a One-Sample T-Test
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Report the test statistic, p-value, and degrees of freedom from technology when performing the test.

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P-Value for a Population Mean Test
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The probability, assuming the null mean is true, of getting the observed result or more extreme.

DAT-3.EDAT-3.E.1
Decision and Conclusion in a Significance Test
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Compare p-value to α to reject or fail to reject, never claiming the null is true.

DAT-3.FDAT-3.F.1
Null and Alternative Hypotheses for a Mean
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Statements about the population mean that define the claim being tested.

DAT-3.F