Practice problems
Problem sets with complete worked solutions. Try each one first, then open the solution and check your steps, not just your answer.
Binomial probability practice problemsPractice binomial probability: exactly, at least, at most, the complement trick, and the mean and standard deviation, with 8 solved AP problems.Boxplot and five-number summary practice 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.Chi-square practice problemsPractice chi-square tests on two-way tables: expected counts, the statistic, degrees of freedom, and homogeneity vs independence, with 8 solved problems.Conditional probability practice problemsPractice conditional probability with 8 AP Statistics problems on two-way tables, the P(A given B) formula, and independence checks, with full solutions.Confidence interval practice problemsEight worked confidence interval problems on one-proportion z-intervals and one-sample t-intervals: construct, interpret, and margin-of-error effects.Expected value and random variable practice problemsPractice discrete random variable mean and standard deviation, fair-game reasoning, and comparing expected values with 8 worked AP-style problems.Proportion z-test practice problemsPractice one-proportion and two-proportion z-tests: hypotheses, conditions, pooled standard error, test statistic, p-value, conclusions. 8 problems.Regression and correlation practice problemsEight worked regression and correlation problems: find the slope and intercept from summary stats, interpret r and r-squared, and compute residuals.Sampling distribution and CLT practice problemsEight practice problems on sampling distributions and the CLT: mean and standard deviation of x-bar and p-hat, probabilities, and normal conditions.Standard deviation and variance practice problemsEight worked standard deviation and variance problems: sample and population SD by hand, the effect of adding a constant, and scaling by a factor.t-test practice problems (one-sample and paired)Practice 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.Z-scores and normal distribution practice problemsPractice z-score conversions, standard normal table areas, percentiles, and the empirical rule with 8 AP-style problems and full step-by-step solutions.