AP®︎ Statistics: Topic 4.9 Flashcards

Master key terms and definitions for Topic 4.9 of AP Statistics – Setting Up a Test for the Difference Between 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 Between Two Population Means

Definition

Test for a difference between two population means using a quantitative response from two independent groups when population standard deviations are unknown

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Two-Sample t-Test for a Difference Between Two Population Means
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Test for a difference between two population means using a quantitative response from two independent groups when population standard deviations are unknown

4.9.A4.9.A.1
μ1 and μ2
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μ1 and μ2 are the population mean values of the quantitative response variable for population 1 and population 2, defined in context

4.9.A4.9.A.2
Order of Subtraction
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Choose an order such as μ1 - μ2 and keep that same order in the parameter definitions, hypotheses, sample difference x̄1 - x̄2, and conclusion

4.9.A4.9.A.2
Null Hypothesis for Two Population Means
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H₀: μ1 - μ2 = 0, equivalently H₀: μ1 = μ2

4.9.B4.9.B.1
Two-Sided Alternative Hypothesis for Two Population Means
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Hₐ: μ1 - μ2 ≠ 0, equivalently Hₐ: μ1 ≠ μ2; used when asking whether the means are different

4.9.B4.9.B.1
Right-Sided Alternative Hypothesis for Two Population Means
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Hₐ: μ1 - μ2 > 0, equivalently Hₐ: μ1 > μ2; used when asking whether population 1 has the greater mean

4.9.B4.9.B.1
Left-Sided Alternative Hypothesis for Two Population Means
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Hₐ: μ1 - μ2 < 0, equivalently Hₐ: μ1 < μ2; used when asking whether population 1 has the smaller mean

4.9.B4.9.B.1
Equality Goes in the Null Hypothesis
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The null uses =, not >, <, or ≠; inequalities belong in the alternative hypothesis

4.9.B4.9.B.1
Hypotheses Use Population Parameters, Not Sample Statistics
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Write hypotheses with μ1 and μ2, not with x̄1 and x̄2

4.9.B4.9.B.1
Randomization Condition
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Data come from two independent random samples or from a randomized experiment with treatments randomly assigned

4.9.C4.9.C.1.i
10% Condition
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When sampling without replacement, each sample must be no more than 10% of its population: n1 ≤ 0.10N1 and n2 ≤ 0.10N2; not needed for a randomized experiment

4.9.C4.9.C.1.ii
Sample Data Condition
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Both samples must have n at least 30, or both populations are approximately normal; if either sample size is less than 30, both sample distributions should be free of strong skewness and outliers

4.9.C4.9.C.1.iii
Independent Groups vs. Matched Pairs
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Two-sample t-tests are for independent groups; matched-pairs data use differences within pairs and then a one-sample t-test for the mean difference

4.9.A4.9.A.1
Means vs. Proportions
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Use a two-sample t-test when comparing population means for a quantitative variable; success/failure data use a two-sample z-test for a difference between proportions

4.9.A4.9.A.1
No Equal-Variance Requirement
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A two-sample t-test does not require equal sample sizes or equal population variances; the AP procedure does not pool the sample variances

4.9.A4.9.A.1