AP®︎ Statistics: Topic 4.4 Flashcards

Master key terms and definitions for Topic 4.4 of AP Statistics – Setting Up a Test for a Population Mean or Population Mean Difference to help you prep for quizzes and the AP exam.

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Term

One-Sample t-Test for a Population Mean

Definition

Significance test for a claim about a population mean μ when one quantitative sample is used and σ is unknown

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One-Sample t-Test for a Population Mean
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Significance test for a claim about a population mean μ when one quantitative sample is used and σ is unknown

4.4.A4.4.A.1
One-Sample t-Test for a Population Mean Difference
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One-sample t-test on the pairwise differences to test a claim about μd, the population mean difference, in a matched-pairs design

4.4.A4.4.A.2
Matched Pairs Design
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Design with two dependent measurements per pair; analyze by computing one difference for each pair and treating those differences as one sample

4.4.A4.4.A.2
Population Parameter for a One-Sample Mean Test
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μ = the population mean of the quantitative response variable for the population in context

4.4.A4.4.A.3
Population Parameter for a Matched-Pairs Mean Difference Test
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μd = the population mean of the pairwise differences for the population in context

4.4.A4.4.A.3
Null and Alternative Hypotheses for One Population Mean
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H₀: μ = μ₀; Hₐ: μ < μ₀, μ > μ₀, or μ ≠ μ₀, chosen from the investigative question

4.4.B4.4.B.1
Null and Alternative Hypotheses for a Population Mean Difference
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H₀: μd = 0; Hₐ: μd < 0, μd > 0, or μd ≠ 0, based on the context and defined differences

4.4.B4.4.B.2
Direction of the Alternative Hypothesis
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Choose μ < μ₀, μ > μ₀, or μ ≠ μ₀ from the investigative question; in matched pairs, choose the direction only after defining the order of subtraction

4.4.B4.4.B.1
Order of Subtraction in Matched Pairs
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The defined difference, such as B − A, must stay consistent because reversing it reverses the meaning of positive and negative differences and the inequality in Hₐ

4.4.B4.4.B.2
Randomization Condition
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Data must come from a random sample or a randomized experiment

4.4.C4.4.C.1.i
10% Condition
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When sampling without replacement, require n/N ≤ 0.10, equivalently N ≥ 10n

4.4.C4.4.C.1.ii
Sample Data Condition
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Condition is met if the population distribution is approximately normal, or n ≥ 30, or if n < 30 the sample data are free of strong skewness and outliers

4.4.C4.4.C.1.iii
Sample Data Condition for Matched Pairs
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Check the number and distribution of the differences, not the two original samples; if the population distribution of differences is approximately normal, or n ≥ 30 differences, or if n < 30 the differences are free of strong skewness and outliers, the condition is met

4.4.C4.4.C.1.iii