AP Statistics

What the course covers

5 units, with exam weights

1. Unit 1

   Exploring One-Variable Data and Collecting Data

   20-30% of examFree
   The start of the statistical problem-solving process: pose an investigative question, identify variables, parameters, and statistics, and describe one-variable categorical and quantitative data with tables, graphs, and summary statistics (shape, center, variability, unusual features). Then collect data well: census, observational studies, and experiments; random sampling methods; the biases that ruin samples; and the experimental designs that justify cause-and-effect conclusions.
   13 topics

   1. 1.1Introducing Statistics: What Can We Learn from Data?
   2. 1.2Variables
   3. 1.3Tabular Representation and Summary Statistics for One Categorical Variable
   4. 1.4Graphical Representations for One Categorical Variable
   5. 1.5Graphical Representations for One Quantitative Variable
   6. 1.6Descriptions for One Quantitative Variable Distributions
   7. 1.7Summary Statistics for One Quantitative Variable
   8. 1.8Graphical Representations of Summary Statistics for One Quantitative Variable
   9. 1.9Comparisons of the Distributions for One Quantitative Variable
   10. 1.10The Investigative Question Revisited and Data Collection
   11. 1.11Random Sampling
   12. 1.12Potential Problems with Sampling
   13. 1.13Experimental Design

2. Unit 2

   Probability, Random Variables, and Probability Distributions

   15-25% of exam
   From two-way tables to the rules of probability: joint, marginal, and conditional relative frequencies, simulation, complements, mutually exclusive and independent events, the multiplication and addition rules. Then discrete random variables with their expected value and standard deviation, the binomial distribution, the normal distribution and the empirical rule, and finally sampling distributions, randomization distributions, and the central limit theorem.
   12 topics

   1. 2.1Tabular and Graphical Representations for the Distributions of Two Categorical Variables
   2. 2.2Summary Statistics for Two Categorical Variables
   3. 2.3Estimating Probabilities Using Simulation
   4. 2.4Introduction to Probability
   5. 2.5Mutually Exclusive Events
   6. 2.6Conditional Probability
   7. 2.7Independent Events and Unions of Events
   8. 2.8Introduction to Random Variables and Probability Distributions
   9. 2.9Parameters of Random Variables
   10. 2.10The Binomial Distribution
   11. 2.11The Normal Distribution
   12. 2.12Sampling Distributions and the Central Limit Theorem

3. Unit 3

   Inference for Categorical Data: Proportions

   15-25% of exam
   Statistical inference begins. Sampling distributions for one and two sample proportions and the conditions that make them approximately normal; one-sample and two-sample z-intervals and z-tests for proportions, with p-values, formal decisions, and conclusions in context; Type I and Type II errors and power; and chi-square tests for homogeneity and independence with expected counts.
   15 topics

   1. 3.1Estimators
   2. 3.2Sampling Distributions for Sample Proportions
   3. 3.3Constructing a Confidence Interval for a Population Proportion
   4. 3.4Justifying a Claim Based on a Confidence Interval for a Population Proportion
   5. 3.5Setting Up a Test for a Population Proportion
   6. 3.6p-Values
   7. 3.7Carrying Out a Test for a Population Proportion
   8. 3.8Potential Errors When Performing Tests
   9. 3.9Sampling Distributions for the Difference Between Sample Proportions
   10. 3.10Constructing a Confidence Interval for the Difference Between Two Population Proportions
   11. 3.11Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Proportions
   12. 3.12Setting Up a Test for the Difference Between Two Population Proportions
   13. 3.13Carrying Out a Test for the Difference Between Two Population Proportions
   14. 3.14Setting Up a Chi-Square Test for Homogeneity or Independence
   15. 3.15Carrying Out a Chi-Square Test for Homogeneity or Independence

4. Unit 4

   Inference for Quantitative Data: Means

   10-20% of exam
   Inference for means when the population standard deviation is unknown: the sampling distribution of a sample mean and of a difference in sample means, t-distributions, one-sample t-intervals and t-tests (including matched pairs through the mean difference), and two-sample t-intervals and t-tests, with the randomization, 10%, and sample data conditions and conclusions tied to p-values or to whether an interval contains 0.
   10 topics

   1. 4.1Sampling Distributions for Sample Means
   2. 4.2Constructing a Confidence Interval for a Population Mean or Population Mean Difference
   3. 4.3Justifying a Claim Based on a Confidence Interval for a Population Mean or Population Mean Difference
   4. 4.4Setting Up a Test for a Population Mean or Population Mean Difference
   5. 4.5Carrying Out a Test for a Population Mean or Population Mean Difference
   6. 4.6Sampling Distributions for the Difference Between Two Sample Means
   7. 4.7Constructing a Confidence Interval for the Difference Between Two Population Means
   8. 4.8Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Means
   9. 4.9Setting Up a Test for the Difference Between Two Population Means
   10. 4.10Carrying Out a Test for the Difference Between Two Population Means

5. Unit 5

   Regression Analysis

   10-20% of exam
   Relationships between two quantitative variables: scatterplots described by form, direction, strength, and unusual features; the correlation coefficient and why it neither guarantees a linear model nor implies causation; predictions from a linear model and the danger of extrapolation; residuals and residual plots; and the least-squares regression line, with slope, intercept, and r-squared interpreted in context.
   5 topics

   1. 5.1Graphical Representations Between Two Quantitative Variables
   2. 5.2Correlation
   3. 5.3Linear Regression Models
   4. 5.4Residuals
   5. 5.5Least-Squares Regression

The exam, part by part

5 parts, 3 h in all.

• Section I: Multiple Choice

  Questions

  42

  Time

  1 h 30 min

  Weight

  50%

  Calculator allowed

  Format details

  Four answer choices (A-D). Mostly discrete questions plus two 3-question sets built on a shared stimulus: one probability and random variables set and one regression set. All five units appear, weighted Unit 1 20-30%, Unit 2 15-25%, Unit 3 15-25%, Unit 4 10-20%, Unit 5 10-20%; by practice, Formulate Questions 5-10%, Collect Data 20-30%, Analyze Data 25-35%, Interpret Results 25-35%. A graphing calculator with statistical capabilities is expected, and the formula sheet and tables are provided.

• Section II, Question 1: Multi-Focus on Practices 1 and 2

  Questions

  1

  Time

  22.5 min

  Weight

  12.5%

  Calculator allowed

  Format details

  Task types: Multi-Focus on Practices 1 and 2

  Section II is one 90-minute block for all four questions; College Board publishes no per-question pacing, so 22.5 minutes is an even share.

• Section II, Question 2: Multi-Focus on Practices 3 and 4

  Questions

  1

  Time

  22.5 min

  Weight

  12.5%

  Calculator allowed

  Format details

  Task types: Multi-Focus on Practices 3 and 4

  Even share of the 90-minute Section II.

• Section II, Question 3: Inference

  Questions

  1

  Time

  22.5 min

  Weight

  12.5%

  Calculator allowed

  Format details

  Task types: Inference

  Even share of the 90-minute Section II. A complete hypothesis test or confidence interval.

• Section II, Question 4: Multi-Focus on Practices 2, 3, and 4

  Questions

  1

  Time

  22.5 min

  Weight

  12.5%

  Calculator allowed

  Format details

  Task types: Multi-Focus on Practices 2, 3, and 4

  Even share of the 90-minute Section II. Spans several units in one scenario.

Skills the exam scores

• 1.AFormulate Questions: pose an investigative question

  Determine a valid investigative question that needs a statistical investigation, naming the variables, the parameter and direction (or estimation goal), and the population. Practice 1 is 5-10% of the multiple-choice section.

• 2.ACollect Data: identify relevant information

  Identify the parts of a study that answer a question: population, sample, variables, study type, sampling method, bias. Practice 2 is 20-30% of the multiple-choice section.

• 2.BCollect Data: justify a data-collection method

  Justify an appropriate and ethical method for gathering and representing data, including sampling designs, experimental designs, and the scope of conclusions.

• 2.CCollect Data: choose the inference method

  Identify the appropriate inference procedure (interval or test, proportions or means, one or two samples, paired, chi-square) and its parameter.

• 2.DCollect Data: errors and relationships in inference

  Identify Type I and Type II errors, power, and how sample size, confidence level, and significance level affect margin of error, width, and error probabilities.

• 2.ECollect Data: state hypotheses

  Identify the null and alternative hypotheses in parameter notation and in words.

• 3.AAnalyze Data: construct representations

  Construct tables and graphs of data and distributions: frequency tables, bar charts, histograms, dotplots, boxplots, scatterplots, probability distributions. Practice 3 is 25-35% of the multiple-choice section.

• 3.BAnalyze Data: summary statistics and predictions

  Calculate summary statistics, relative positions such as z-scores and percentiles, and predicted responses from a regression model.

• 3.CAnalyze Data: probabilities and intervals

  Calculate or estimate expected counts, percentages, probabilities, and intervals, including simulation, binomial, and normal calculations.

• 3.DAnalyze Data: parameters of distributions

  Calculate means, standard deviations, and other parameters of probability distributions and sampling distributions.

• 3.EAnalyze Data: inference results

  Calculate test statistics, p-values, confidence intervals, standard errors, and margins of error.

• 4.AInterpret Results: describe and compare displays

  Describe and compare tables, graphs, and summary statistics in context. Practice 4 is 25-35% of the multiple-choice section.

• 4.BInterpret Results: justify a claim from calculations

  Justify a claim using statistical calculations and results, with explicit numerical evidence.

• 4.CInterpret Results: distributions and relative position

  Describe distributions (including normal, t, chi-square, and sampling distributions) and compare relative positions of values.

• 4.DInterpret Results: interpret calculations

  Interpret statistical calculations in context to assess meaning or a claim: expected values, standard deviations, probabilities, residuals, slope, correlation, r-squared.

• 4.EInterpret Results: verify conditions

  Justify the use of an inference procedure by verifying its conditions with evidence from the context.

• 4.FInterpret Results: interpret inference

  Interpret confidence intervals, confidence levels, and p-values in context.

• 4.GInterpret Results: justify a claim from inference

  Justify a claim from inference results: a formal decision linked to the p-value, or a claim supported by the values in a confidence interval.