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References for Inference for Means

Curated resources to deepen your understanding of t-distributions and inference procedures for population means.

Wikipedia Articles

  1. Student's t-test - Wikipedia - Comprehensive overview of the t-test including its history, derivation by William Gosset at Guinness Brewery, and various applications for one-sample and two-sample hypothesis testing.

  2. Student's t-distribution - Wikipedia - Detailed explanation of the t-distribution's properties, including its relationship to the normal distribution, degrees of freedom, and why heavier tails account for uncertainty when estimating population standard deviation.

  3. Welch's t-test - Wikipedia - Explains the unpooled two-sample t-test that does not assume equal variances, including the Welch-Satterthwaite approximation for degrees of freedom used in AP Statistics.

Textbooks

  1. The Practice of Statistics by Starnes, Tabor, Yates, and Moore - W.H. Freeman (2018) - The standard AP Statistics textbook with thorough coverage of t-procedures, conditions checking, and worked examples aligned with AP exam expectations.

  2. Statistics: Learning from Data by Roxy Peck and Tom Short - Cengage Learning (2018) - Clear explanations of one-sample t-intervals, two-sample t-tests, and paired t-procedures with emphasis on real-world applications and interpretation.

Online Resources

  1. AP Statistics Course and Exam Description - College Board - The official guide to AP Statistics content, including detailed learning objectives for inference procedures and sample free-response questions with scoring guidelines.

  2. Khan Academy: Significance Tests (Hypothesis Testing) - Khan Academy - Free video lessons covering t-tests for means with step-by-step calculations, visual explanations, and practice problems with immediate feedback.

  3. Stat Trek: Student's t Distribution - Stat Trek - Clear tutorial on t-distribution properties, t-tables, and calculating t-critical values with interactive examples suitable for high school students.

  4. Against All Odds: Inside Statistics - Annenberg Learner - Video series hosted by Pardis Sabeti covering inference for means with real-world examples including medical research and quality control applications.

  5. OpenIntro Statistics - OpenIntro - Free open-source textbook with chapters on inference for one mean and paired data, including worked examples and end-of-chapter exercises with solutions.