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Browse all available quizzes, quizbooks, articles, textbooks, SynLearn templates, and SynPrep practice tracks.

1890 learning items

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Quiz

Vectors, Matrix Arithmetic & Linear Systems

Build the matrix language needed for statistical models. Practice vector products, norms, transposes, compatible dimensions, matrix arithmetic, linear systems, rank, independence and inverses. Prerequisites: algebra and basic statistical notation. Move from small calculations to design-matrix identification and existence-versus-uniqueness reasoning, with worked solutions and misconception-based alternatives. Further reading: [Interactive Linear Algebra](https://textbooks.math.gatech.edu/ila/matrix-multiplication.html).

statistics

Oct 24, 2026

20 questions

Quiz

Dedicated Normality Tests & Visual Diagnostics

Build a practical normality diagnostic toolkit using Shapiro–Wilk, Anderson–Darling, Jarque–Bera and normal Q–Q plots. Work through statistic calculations, tail and skew patterns, calibration, power and reporting pitfalls. Prerequisites: distributions, skewness and kurtosis, hypothesis testing and continuous goodness of fit. Original scenarios and counterexamples connect diagnostic evidence to the analysis it is meant to support. Further reading: [NIST normality tests](https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm), [NIST normal probability plots](https://www.itl.nist.gov/div898/handbook/eda/section3/normprpl.htm).

statistics

Oct 24, 2026

25 questions

Quiz

p-Values: Computation, Meaning & Traps

Compute and interpret p-values without confusing evidence, effect size or hypothesis probability. Contrast tail rules, examine discrete and continuous calibration, and apply transparent reporting principles. Prerequisites: probability, sample summaries, normal and t distributions, and basic algebra. Original questions include worked reasoning and content-based distractor explanations. Progress from core calculations to assumption checks and analytical decisions. References: [Source 1](https://www.amstat.org/asa/files/pdfs/p-valuestatement.pdf), [Source 2](https://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 24, 2026

25 questions

Quiz

Type I Error, Type II Error & Statistical Power

Understand testing errors and statistical power as conditional repeated-sampling probabilities. Calculate examples, interpret power curves and evaluate changes in noise, sample size and decision thresholds. Prerequisites: probability, sample summaries, normal and t distributions, and basic algebra. Original questions include worked reasoning and content-based distractor explanations. Progress from core calculations to assumption checks and analytical decisions. References: [Source 1](https://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 24, 2026

30 questions

Quiz

Hypotheses, Test Statistics & Decision Rules

Build hypothesis tests from scientific questions, parameter statements and prespecified decision rules. Practice directional alternatives, standardized distances, critical regions and responsible conclusions. Prerequisites: probability, sample summaries, normal and t distributions, and basic algebra. Original questions include worked reasoning and content-based distractor explanations. Progress from core calculations to assumption checks and analytical decisions. References: [Source 1](https://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm), [Source 2](https://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 24, 2026

25 questions

Quiz

Sample Size Determination for Desired Margin of Error

Plan samples for a desired estimation margin. Calculate and round requirements, evaluate assumptions about variability, and account for finite-population sampling, response yield and design effects. Prerequisites: probability, sample summaries, normal and t distributions, and basic algebra. Original questions include worked reasoning and content-based distractor explanations. Progress from core calculations to assumption checks and analytical decisions. References: [Source 1](https://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 24, 2026

20 questions

Quiz

Confidence Intervals for Population Variance & Variance Ratios

Quantify uncertainty in population variability through chi-square and F pivots. Invert quantiles carefully, transform positive parameters and distinguish variance units from standard-deviation units. Prerequisites: probability, sample summaries, normal and t distributions, and basic algebra. Original questions include worked reasoning and content-based distractor explanations. Progress from core calculations to assumption checks and analytical decisions. References: [Source 1](https://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm), [Source 2](https://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 24, 2026

20 questions

Quiz

Confidence Intervals for Population Proportions

Estimate binary probabilities and differences using Wald, Wilson score and adjusted-Wald ideas. Examine boundary counts, interval inversion, percent units and limitations of binomial approximations. Prerequisites: probability, sample summaries, normal and t distributions, and basic algebra. Original questions include worked reasoning and content-based distractor explanations. Progress from core calculations to assumption checks and analytical decisions. References: [Source 1](https://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 24, 2026

30 questions

Quiz

Confidence Intervals for Differences in Two Means

Compare independent populations and matched observations through Welch, pooled and paired t intervals. Calculate contrasts, standard errors and degrees of freedom while preserving the study design. Prerequisites: probability, sample summaries, normal and t distributions, and basic algebra. Original questions include worked reasoning and content-based distractor explanations. Progress from core calculations to assumption checks and analytical decisions. References: [Source 1](https://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 24, 2026

30 questions

Quiz

Confidence Interval for a Single Population Mean

Estimate a population mean with known-scale z and unknown-scale t intervals. Work through standard errors, quantiles, interval arithmetic and the distinction between uncertainty about a mean and variation in individual outcomes. Prerequisites: probability, sample summaries, normal and t distributions, and basic algebra. Original questions include worked reasoning and content-based distractor explanations. Progress from core calculations to assumption checks and analytical decisions. References: [Source 1](https://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 24, 2026

30 questions

Quiz

Philosophy & Interpretation of Confidence Intervals

Build a precise interpretation of confidence procedures before learning specialized interval recipes. Explore pivotal quantities, repeated coverage, margins of error, simulation uncertainty, selection effects and the distinction between confidence and prediction. Prerequisites: Sampling distributions, standard errors and the normal, t and chi-square reference laws. Includes single-select and multiselect practice with worked explanations and misconception analysis. Questions are independently answerable; local learning order progresses from foundations to analytical challenges.

statistics

Oct 24, 2026

20 questions

Quiz

Order Statistics & Extremes

Analyze sorted random samples through minima, maxima, medians and general ranks. Derive event probabilities, use uniform order-statistic beta laws, and explore transformed ranks, bias correction and dependence between extremes. Prerequisites: CDFs, independence, differentiation, binomial probabilities and beta distributions. Includes single-select and multiselect practice with worked explanations and misconception analysis. Questions are independently answerable; local learning order progresses from foundations to analytical challenges.

statistics

Oct 24, 2026

20 questions