AP-STAT
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AP® Statistics
AP Statistics teaches students to explore, analyze, and interpret data using statistical concepts, probability, and sampling distributions, preparing them for college-level statistics and data-driven decision making.
180
Minutes
46
Questions
3/5
Passing Score
$98
Exam Cost
Who Should Take This
High school juniors and seniors planning to pursue college majors in science, engineering, economics, or social sciences should take this exam. It suits learners with basic algebra skills who seek to master statistical reasoning, hypothesis testing, and data analysis to strengthen college applications and future coursework.
What's Covered
1
Unit 1: Exploring One-Variable Data
2
Unit 2: Exploring Two-Variable Data
3
Unit 3: Collecting Data
4
Unit 4: Probability, Random Variables, and Probability Distributions
5
Unit 5: Sampling Distributions
6
Unit 6: Inference for Categorical Data — Proportions
7
Unit 7: Inference for Quantitative Data — Means
8
Unit 8: Inference for Categorical Data — Chi-Square
9
Unit 9: Inference for Quantitative Data — Slopes
What's Included in AccelaStudy® AI
Adaptive Knowledge Graph
Practice Questions
Lesson Modules
Console Simulator Labs
Exam Tips & Strategy
20 Activity Formats
Course Outline
60 learning goals
1
Unit 1: Exploring One-Variable Data
3 topics
Graphical Displays and Distribution Shape
- Identify and construct appropriate graphical displays (dotplots, histograms, stemplots, boxplots, ogives) for one-variable quantitative data and describe the features of the resulting distribution.
- Describe the shape of a distribution using standard terminology (symmetric, skewed left, skewed right, uniform, bimodal, unimodal) and explain how shape affects the relationship between mean and median.
Numerical Summaries
- Calculate and interpret measures of center (mean, median) and measures of spread (range, IQR, standard deviation, variance) for a dataset, selecting the appropriate summary based on distribution shape.
- Identify potential outliers using the 1.5 times IQR rule or the two-standard-deviation criterion and explain the effect of outliers on summary statistics including mean, median, range, and standard deviation.
- Compare distributions of two or more groups using parallel boxplots or back-to-back stemplots, discussing differences in center, spread, shape, and unusual features in context.
Normal Distributions
- Describe the properties of the normal distribution including the empirical rule (68-95-99.7) and calculate z-scores to standardize individual observations for comparison across different distributions.
- Use the standard normal distribution table or calculator functions to find proportions, percentiles, and boundary values for normally distributed data, interpreting results in context.
- Assess whether a dataset is approximately normally distributed using normal probability plots and empirical rule checks, explaining the implications for subsequent statistical analysis.
2
Unit 2: Exploring Two-Variable Data
2 topics
Scatterplots and Correlation
- Construct and describe scatterplots for bivariate quantitative data, identifying the direction, form, and strength of the association and noting any unusual features such as clusters or outliers.
- Interpret the correlation coefficient r as a measure of the strength and direction of a linear relationship, explaining its properties including the range from negative one to one and its lack of units.
- Explain why correlation does not imply causation and identify potential confounding variables, lurking variables, and common sources of misinterpretation in observational associations.
Regression and Residuals
- Calculate and interpret the least-squares regression line equation, explaining the meaning of the slope and y-intercept in the context of the data.
- Calculate residuals, construct and interpret residual plots to assess the appropriateness of a linear model, and identify patterns that suggest a non-linear relationship.
- Interpret the coefficient of determination r-squared as the proportion of variation in the response variable explained by the explanatory variable in the regression model.
- Identify influential points (high leverage and high influence) in a regression analysis and analyze how their removal affects the slope, y-intercept, and correlation coefficient.
- Apply logarithmic and power transformations to linearize curved relationships, fit regression models to transformed data, and use the model to make predictions in the original units.
3
Unit 3: Collecting Data
2 topics
Sampling Methods and Bias
- Describe the principles of random sampling and identify the key features of simple random samples, stratified random samples, cluster samples, and systematic samples.
- Identify and explain sources of bias in sampling including undercoverage, nonresponse bias, response bias, and voluntary response bias, describing how each affects the validity of conclusions.
- Evaluate a proposed sampling plan for a specific research question, identifying potential sources of bias and recommending improvements to the design.
Experimental Design
- Distinguish between observational studies and experiments, explaining why only well-designed experiments can establish causal relationships between variables.
- Identify and describe the principles of experimental design: control, randomization, replication, and blocking, explaining the purpose of each in reducing bias and variability.
- Design a completely randomized experiment or a randomized block design for a given research scenario, specifying treatments, response variables, and control procedures.
- Explain the purpose and proper use of blinding, double-blinding, placebo groups, and matched pairs designs in reducing confounding and improving internal validity.
- Evaluate the scope of inference (generalizability and causation) that can be drawn from a study based on how data were collected, distinguishing between random sampling and random assignment.
4
Unit 4: Probability, Random Variables, and Probability Distributions
2 topics
Probability Rules and Concepts
- State the basic probability rules (complement, addition, multiplication) and apply them using tree diagrams, Venn diagrams, and two-way tables to calculate probabilities of compound events.
- Calculate and interpret conditional probabilities using the formula P(A|B) = P(A and B)/P(B) and determine whether two events are independent by comparing conditional and unconditional probabilities.
- Apply probability concepts to solve multi-step problems involving independent and dependent events, using simulation to estimate probabilities when analytical solutions are complex.
Random Variables and Distributions
- Define discrete and continuous random variables, construct probability distributions for discrete random variables, and calculate expected value (mean) and standard deviation from the distribution.
- Apply the rules for combining independent random variables to calculate the mean and standard deviation of sums and differences of random variables.
- Identify scenarios that satisfy the conditions for a binomial distribution, calculate binomial probabilities using the formula and calculator functions, and compute the mean and standard deviation.
- Identify scenarios that satisfy the conditions for a geometric distribution, calculate geometric probabilities, and determine the expected number of trials until the first success.
- Construct probability models for real-world scenarios by selecting the appropriate distribution (binomial, geometric, normal) and justifying the choice based on the conditions of the experiment.
5
Unit 5: Sampling Distributions
1 topic
Sampling Distributions and the Central Limit Theorem
- Describe the concept of a sampling distribution and distinguish between the distribution of a population, the distribution of a sample, and the sampling distribution of a statistic.
- Describe the sampling distribution of a sample proportion including its mean, standard deviation, and the conditions under which it is approximately normal.
- State the Central Limit Theorem and explain how it justifies the use of normal-based inference procedures for sample means regardless of the population distribution when the sample size is sufficiently large.
- Describe the sampling distribution of a sample mean including its mean, standard deviation, and shape, applying the Central Limit Theorem to determine when the normal approximation is appropriate.
- Calculate probabilities involving sample means and sample proportions using their sampling distributions and interpret the results in the context of the sampling process.
6
Unit 6: Inference for Categorical Data — Proportions
2 topics
Confidence Intervals for Proportions
- Construct and interpret a confidence interval for a single population proportion, checking the conditions of randomness, independence (10% condition), and normality (large counts condition).
- Interpret the confidence level as the long-run capture rate of the interval procedure and explain why increasing the confidence level widens the interval while increasing sample size narrows it.
- Determine the sample size needed to achieve a desired margin of error for a confidence interval for a proportion, using conservative and estimated values of the population proportion.
Hypothesis Tests for Proportions
- Conduct a significance test for a single population proportion by stating hypotheses, checking conditions, computing the test statistic and p-value, and stating a conclusion in context.
- Interpret the p-value as the probability of obtaining results at least as extreme as the observed results under the null hypothesis, and distinguish between statistical significance and practical significance.
- Explain Type I and Type II errors in the context of a hypothesis test, describe the relationship between significance level and error probabilities, and define the power of a test.
- Construct a confidence interval and conduct a significance test for the difference of two population proportions, checking conditions and interpreting results in the context of the study.
7
Unit 7: Inference for Quantitative Data — Means
2 topics
Inference for a Single Mean
- Describe the t-distribution, explain how it differs from the standard normal distribution, and identify how degrees of freedom affect its shape.
- Construct and interpret a confidence interval for a single population mean using the t-distribution, checking the conditions of randomness, independence, and normality of the sampling distribution.
- Conduct a significance test for a single population mean using the t-distribution by stating hypotheses, checking conditions, computing the test statistic and p-value, and stating conclusions in context.
Comparing Two Means
- Construct a confidence interval and conduct a significance test for the difference of two independent population means using the two-sample t-procedures, checking the required conditions.
- Conduct a paired t-test by computing differences within matched pairs, treating the differences as a single sample, and performing a one-sample t-procedure on the differences.
- Design and execute a complete inference study for comparing two group means, selecting the appropriate procedure (independent or paired), justifying the choice, and interpreting the results in context.
8
Unit 8: Inference for Categorical Data — Chi-Square
1 topic
Chi-Square Tests
- Describe the chi-square distribution, explain how degrees of freedom affect its shape, and state the conditions required for chi-square inference (random, independent, large expected counts).
- Conduct a chi-square goodness-of-fit test to determine whether the distribution of a categorical variable matches a hypothesized distribution, computing expected counts and the test statistic.
- Conduct a chi-square test for independence to determine whether there is an association between two categorical variables in a single population, using a two-way table of observed and expected counts.
- Conduct a chi-square test for homogeneity to determine whether the distribution of a categorical variable is the same across two or more populations or treatments.
- Compare and contrast the chi-square test for independence and the chi-square test for homogeneity, explaining how the data collection method determines which test is appropriate.
9
Unit 9: Inference for Quantitative Data — Slopes
1 topic
Inference for Regression
- State the conditions for inference about the slope of a least-squares regression line (linearity, independence, normality of residuals, equal variance) and describe methods for checking each condition.
- Construct and interpret a confidence interval for the slope of a population regression line using the t-distribution, the standard error of the slope, and the appropriate degrees of freedom.
- Conduct a significance test for the slope of a population regression line by stating hypotheses, computing the t-test statistic, finding the p-value, and stating conclusions in context.
- Interpret computer output from a regression analysis, identifying the estimated slope, intercept, standard errors, t-statistics, p-values, and r-squared, and use them to perform inference.
- Synthesize exploratory data analysis, study design, probability, and inference to plan and execute a complete statistical investigation from data collection through inference and contextual interpretation.
Scope
Included Topics
- All nine units of the AP Statistics course framework (College Board, effective 2020-present): Unit 1 Exploring One-Variable Data, Unit 2 Exploring Two-Variable Data, Unit 3 Collecting Data, Unit 4 Probability, Random Variables, and Probability Distributions, Unit 5 Sampling Distributions, Unit 6 Inference for Categorical Data: Proportions, Unit 7 Inference for Quantitative Data: Means, Unit 8 Inference for Categorical Data: Chi-Square, Unit 9 Inference for Quantitative Data: Slopes.
- Exploring one-variable data: describing and comparing distributions of data using graphical displays (dotplots, histograms, stemplots, boxplots, ogives), measures of center (mean, median, mode), measures of spread (range, IQR, standard deviation, variance), identifying outliers, and describing the shape of distributions (symmetric, skewed, uniform, bimodal).
- Exploring two-variable data: scatterplots, correlation coefficient, least-squares regression lines, residual plots, coefficient of determination (r-squared), influential points, and transformations to achieve linearity (logarithmic and power models).
- Collecting data: census, sample surveys, observational studies, experiments, random sampling methods (SRS, stratified, cluster, systematic), sources of bias (undercoverage, nonresponse, response bias, voluntary response), principles of experimental design (control, randomization, replication, blocking), and completely randomized and randomized block designs.
- Probability: basic probability rules, conditional probability, independence, multiplication and addition rules, tree diagrams, Venn diagrams, two-way tables, Bayes' theorem concepts, and simulation-based probability estimation.
- Random variables and probability distributions: discrete and continuous random variables, expected value and standard deviation, combining independent random variables, binomial distributions, geometric distributions, and the normal distribution including z-scores and the empirical rule.
- Sampling distributions: sampling distribution of a sample proportion, sampling distribution of a sample mean, the Central Limit Theorem, and the concept of standard error.
- Inference for proportions: confidence intervals and hypothesis tests for a single proportion and for the difference of two proportions, conditions for inference, interpretation of confidence levels and p-values.
- Inference for means: confidence intervals and hypothesis tests for a single mean and for the difference of two means (paired and independent), t-distributions, and conditions for inference.
- Chi-square tests: chi-square goodness-of-fit test, chi-square test for independence, chi-square test for homogeneity, expected counts, degrees of freedom, and conditions for chi-square inference.
- Inference for regression slopes: confidence intervals and hypothesis tests for the slope of a regression line, standard error of the slope, and conditions for inference about regression.
- Exam-aligned skills including interpreting statistical results in context, communicating statistical reasoning, and using technology (calculators and tables) as tested in AP Statistics free-response and multiple-choice questions.
Not Covered
- Non-parametric statistical methods (Mann-Whitney, Kruskal-Wallis, Wilcoxon) beyond the AP Statistics framework.
- Bayesian inference, Bayesian statistics, and posterior probability calculations beyond the conceptual introduction of Bayes' theorem.
- Multivariate regression, ANOVA, and analysis of covariance techniques beyond the single-predictor linear model.
- Advanced probability theory including moment-generating functions, measure theory, and stochastic processes.
- Time series analysis, survival analysis, and other specialized statistical methods.
Official Exam Page
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