AP Statistics

CED topics 1.1 Introducing Statistics: What Can We Learn from Data?, 1.2 Variables. Covers the role of statistics, population vs sample, parameter vs statistic, categorical vs quantitative variables, and the investigative process.

CED topics 1.3 Tabular Representation and Summary Statistics for One Categorical Variable, 1.4 Graphical Representations for One Categorical Variable. Covers frequency tables, relative frequency, bar charts, pie charts, and two-way tables.

CED topics 1.5 Graphical Representations for One Quantitative Variable, 1.6 Summary Statistics for One Quantitative Variable. Covers dotplots, histograms, stemplots, boxplots; measures of center (mean, median, mode), spread (range, IQR, standard deviation, variance), and shape (skewness, modality).

CED topics 1.7 The Investigative Question Revisited and Data Collection, 1.8 Random Sampling and Experimental Design. Covers observational studies vs experiments, sampling methods (SRS, stratified, cluster, systematic), bias, principles of experimental design (random assignment, control, replication, blinding), and completely randomized vs block designs.

CED topics 2.1 Estimating Probabilities Using Simulation, 2.2 Introduction to Probability. Covers simulation methods, the law of large numbers, sample spaces, events, probability rules (addition, complement), and mutually exclusive events.

CED topics 2.3 Conditional Probability, 2.4 Independent Events and Unions of Events. Covers conditional probability, the multiplication rule, independence vs dependence, and the general addition rule for unions.

CED topics 2.5 Introduction to Random Variables and Probability Distributions, 2.6 The Binomial Distribution. Covers discrete vs continuous random variables, probability distributions, expected value and standard deviation of a random variable, and the binomial distribution (conditions, formula, mean, standard deviation).

CED topics 2.7 The Normal Distribution, 2.8 The Geometric Distribution. Covers the properties of the normal distribution, the empirical rule (68-95-99.7), z-scores, standard normal table, normal approximation to binomial, and the geometric distribution.

CED topics 3.1 Estimators, 3.2 Sampling Distributions for Sample Proportions. Covers unbiased estimators, sampling variability, the sampling distribution of p-hat, the central limit theorem for proportions, and conditions (random, 10%, normal).

CED topics 3.3 Constructing a Confidence Interval for a Population Proportion, 3.4 Justifying a Claim Based on a Confidence Interval. Covers the structure of a confidence interval, critical values (z*), margin of error, interpretation of confidence level, and using intervals to evaluate claims.

CED topics 3.5 Setting Up a Test for a Population Proportion, 3.6 p-Values. Covers null and alternative hypotheses, one-tailed vs two-tailed tests, the p-value approach, significance level, and making conclusions in context.

CED topics 3.7 Carrying Out a Test for a Population Proportion, 3.8 Potential Errors When Performing Tests. Covers the full hypothesis test procedure for a proportion, Type I and Type II errors, power of a test, and the relationship between alpha and beta.

CED topics 3.9 Sampling Distributions for the Difference Between Sample Proportions, 3.10 Constructing a Confidence Interval for the Difference Between Two Population Proportions. Covers the sampling distribution of p-hat1 - p-hat2, conditions for inference, two-proportion z-intervals, and two-proportion z-tests.

CED topics 4.1 Sampling Distributions for Sample Means, 4.2 Constructing a Confidence Interval for a Population Mean. Covers the central limit theorem for means, the t-distribution, degrees of freedom, and constructing t-intervals for a population mean.

CED topics 4.3 Setting Up a Test for a Population Mean, 4.4 Carrying Out a Test for a Population Mean. Covers setting up null and alternative hypotheses for means, the t-test for a mean, conditions (random, 10%, normal), and computing t-statistics and p-values.

CED topics 4.5 Sampling Distributions for the Difference Between Two Sample Means, 4.6 Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Means. Covers the sampling distribution of x-bar1 - x-bar2, two-sample t-intervals, and two-sample t-tests.

CED topic 4.7 Carrying Out a Test for the Difference Between Two Population Means. Covers the full two-sample t-test procedure, paired t-tests vs independent samples t-tests, and interpreting results in context.

CED topics 5.1 Graphical Representations Between Two Quantitative Variables, 5.2 Correlation. Covers scatterplots, identifying form/direction/strength, the correlation coefficient r, properties of r, and the distinction between correlation and causation.

CED topics 5.3 Linear Regression Models, 5.4 Least-Squares Regression. Covers the least-squares regression line, interpreting slope and y-intercept, residuals and residual plots, the coefficient of determination (r²), extrapolation, and influential points.