Practice problems
424 problems across 53 sets, every one with the full solution worked out. Try each on paper first, then open the steps and check your working, not just your answer.
Unit 1: Exploring One-Variable Data and Collecting Data
20-30% of the exam
Identifying bias practice problems (8 solved)8 problemsEight solved problems on identifying bias in a study: name the type, predict the direction of the error, and see why a bigger sample never removes it.Boxplot and five-number summary practice problems8 problemsPractice quartiles, IQR, the 1.5 IQR outlier rule, and reading and comparing boxplots with 8 AP Statistics problems and full step-by-step solutions.Categorical data practice: tables and graphs8 problemsPractice frequency and relative frequency tables, bar graphs, and pie charts for one categorical variable, with 8 AP Statistics problems and full solutions.Comparing two distributions practice problems8 problemsPractice comparing two distributions with 8 AP Statistics problems on shape, center, variability, and outliers, each with a model full-credit comparison.Describing and comparing distributions practice8 problemsPractice describing shape, center, spread, and unusual features in context and comparing two distributions, with 8 AP Statistics problems and full solutions.Experimental design practice problems (8)8 problemsPractice AP Statistics experimental design: 8 solved problems on completely randomized, block, and matched pairs designs, blinding, confounding, and causation.Investigative question practice (8 problems)8 problemsEight solved problems on turning a vague wondering into an answerable statistical question, deciding what data would answer it, and picking the collection method.Dotplot, stemplot, and histogram practice8 problemsPractice building and reading dotplots, stemplots, and histograms, and seeing how bin width and boundary rules change the shape, with 8 problems and solutions.Quartiles, IQR, and outliers practice problems8 problemsPractice quartiles, the IQR, the 1.5 IQR outlier rule, and modified boxplots with 8 AP Statistics problems worked step by step from the sorted data.Sampling methods practice problems8 problemsPractice naming SRS, stratified, cluster, systematic, convenience, and voluntary response designs, identifying the bias, and stating what a result covers.Scope of inference practice problems (8 solved)8 problemsEight solved problems on scope of inference: when a study supports cause and effect, when it generalizes to a population, and how to word the conclusion.Standard deviation and variance practice problems8 problemsEight worked standard deviation and variance problems: sample and population SD by hand, the effect of adding a constant, and scaling by a factor.Choosing mean vs median and SD vs IQR8 problemsEight problems on choosing the mean or the median and the SD or the IQR, justifying the choice from the distribution, and predicting how each summary moves.Classifying variables practice problems8 problemsPractice classifying variables as categorical or quantitative and discrete or continuous, with 8 AP Statistics topic 1.2 problems and full solutions.Unit 2: Probability, Random Variables, and Probability Distributions
15-25% of the exam
Binomial probability practice problems8 problemsPractice binomial probability: exactly, at least, at most, the complement trick, and the mean and standard deviation, with 8 solved AP problems.Conditional probability practice problems8 problemsPractice conditional probability with 8 AP Statistics problems on two-way tables, the P(A given B) formula, and independence checks, with full solutions.Expected value and random variable practice problems8 problemsPractice discrete random variable mean and standard deviation, fair-game reasoning, and comparing expected values with 8 worked AP-style problems.Independent events practice problems with full solutions8 problemsEight solved problems on testing independence with the product test and the conditional test, plus mutually exclusive events and sampling without replacement.Normal distribution practice problems and solutions8 problemsEight applied normal distribution problems with full solutions: tail and between areas, out-of-spec percents, expected counts, and solving backward for a parameter.Probability rules practice problems8 problemsPractice the addition rule, complements, and independence with 8 AP Statistics problems on unions, at-least-one questions, and two-way tables, fully solved.Discrete random variable practice problems8 problemsEight discrete random variable practice problems: check a valid probability distribution, find a missing probability, and compute the mean and standard deviation.Sampling distribution and CLT practice problems8 problemsEight practice problems on sampling distributions and the CLT: mean and standard deviation of x-bar and p-hat, probabilities, and normal conditions.Simulation practice problems with random digit tables8 problemsEight solved problems on designing and reading simulations: assigning digits, discarding, defining a trial, estimating from trials, and judging a surprising result.Tree diagram probability practice problems8 problemsPractice tree diagrams with 8 problems on multiplying along branches, adding across paths, sampling without replacement, and reversing a conditional.Two-way table probability practice problems8 problemsPractice joint, marginal, and conditional probability with 8 two-way table problems, including completing a table and judging association, with full solutions.Z-scores and normal distribution practice problems8 problemsPractice z-score conversions, standard normal table areas, percentiles, and the empirical rule with 8 AP-style problems and full step-by-step solutions.Unit 3: Inference for Categorical Data: Proportions
15-25% of the exam
Chi-square practice problems8 problemsPractice chi-square tests on two-way tables: expected counts, the statistic, degrees of freedom, and homogeneity vs independence, with 8 solved problems.Chi-square two-way table practice problems8 problemsChi-square practice on two-way tables: expected counts, the statistic term by term, degrees of freedom, and homogeneity vs independence, all fully solved.Checking conditions for inference practice8 problemsVerify Random, 10%, Large Counts, the sample data condition, and expected counts with real numbers. 8 solved problems, including four where a condition fails.Interpreting confidence intervals: practice problems8 problemsEight practice problems on interpreting confidence intervals: write the interval and the confidence level in context, name the wrong readings, and judge claims.Justifying claims: confidence interval practice8 problemsEight practice problems on justifying a claim from a confidence interval: which values it rules out, what an interval containing 0 settles, and how to write it.P-value interpretation practice problems8 problemsA p-value is the probability of a result at least this extreme assuming the null is true. 8 solved problems on reading, computing, and misreading p-values.Proportion z-test practice problems8 problemsPractice one-proportion and two-proportion z-tests: hypotheses, conditions, pooled standard error, test statistic, p-value, conclusions. 8 problems.Margin of error and sample size practice problems8 problemsEight practice problems on margin of error and sample size: compute the margin from a critical value and standard error, then solve for the sample size you need.Sampling distribution of p-hat practice problems8 problemsEight practice problems on the sampling distribution of p-hat: mean and standard deviation, the large counts and 10% conditions, and probabilities from a z-score.Two-proportion z interval and z test practice problems8 problemsPractice two-proportion z intervals and z tests: the pooled standard error, Large Counts on both samples, and reading an interval that contains 0. 8 problems.Type I and Type II Error Practice Problems8 problemsPractice naming Type I and Type II errors in context with 8 solved problems on error consequences, alpha, sample size, and what moves statistical power.Unit 4: Inference for Quantitative Data: Means
10-20% of the exam
One-sample t interval practice: 8 problems8 problemsEight one-sample t interval problems for a mean: find t* on the table, build and interpret the interval, and see what moves the margin of error.Difference of two sample means practice8 problemsEight practice problems on the sampling distribution of the difference between two sample means: its center, why the variances add, shape, and probabilities.Justifying claims from a mean CI: practice8 problemsEight problems on justifying a claim from a confidence interval for a mean or mean difference: which values stay plausible, when zero matters, paired or not.Inference for means: 8 mixed t procedure problems8 problemsEight mixed problems on inference for means. Each one makes you pick the procedure first: one-sample t interval, one-sample t test, two-sample t, or paired t.Paired t test practice: 8 problems with solutions8 problemsEight paired t problems: spot a paired design, build the column of differences, and run the one-sample t procedure on it, with intervals and p-values worked out.Sampling distribution of x-bar: 8 practice problems8 problemsEight practice problems on the sampling distribution of the sample mean: its center, sigma over root n, when the normal model applies, and probabilities about x-bar.t-test practice problems (one-sample and paired)8 problemsPractice one-sample and paired t-tests: 8 solved problems with hypotheses, the t statistic, degrees of freedom, and p-value ranges read from a t-table.Two-sample t test practice problems and intervals8 problemsPractice two-sample t tests and intervals for a difference of means: 8 solved problems with conditions on both samples, conservative df, and p-value ranges.Unit 5: Regression Analysis
10-20% of the exam
Correlation and residual plot practice problems8 problemsEight solved problems on interpreting r and r-squared in context, computing residuals, reading a residual plot for a poor fit, and influential points.Influential points and outliers: regression practice8 problemsEight problems that separate outliers, high-leverage points, and influential points in regression by refitting the slope with and without the suspect point.Computer regression output practice problems8 problemsEight solved problems on reading software regression output: write the equation from the Coef column, predict, find a residual, and turn R-Sq into r.Regression and correlation practice problems8 problemsEight worked regression and correlation problems: find the slope and intercept from summary stats, interpret r and r-squared, and compute residuals.Residual plot practice problems with full solutions8 problemsEight solved problems on residuals: compute observed minus predicted, read the sign, add residuals to zero, and judge a line from the shape of its residual plot.Scatterplot practice problems with full solutions8 problemsEight solved scatterplot problems: pick the explanatory variable, describe form, direction, strength and unusual features, and spot influential points.Across the course
spans more than one unit
Confidence interval practice problems8 problemsEight worked confidence interval problems on one-proportion z-intervals and one-sample t-intervals: construct, interpret, and margin-of-error effects.Mixed inference practice: choosing the procedure8 problemsPractice picking the right inference procedure across AP Units 3 and 4: 8 scenarios covering z-tests, z-intervals, one-sample, paired and two-sample t, chi-square.