AP Statistics

Tips

AP Statistics covers exploring data, sampling and experimental design, probability and random variables, sampling distributions, and inference — confidence intervals and significance tests. There is little algebra; the difficulty is saying the right thing about uncertainty.

Every inference answer has four parts: name the procedure, check the conditions, compute, and conclude in context with a link to the alternative hypothesis. The rubric grades all four, so a correct p-value alone scores poorly.

Language is graded. "We reject H₀" is not "we prove H₁"; a confidence interval is about the method's long-run behaviour, not the probability that a particular interval contains the parameter. These distinctions decide marks.

The notes work through all nine units with each inference procedure set out step by step. Released FRQs are in the library. Statistics gives marks for stating the conditions and interpreting in context, so every worked answer names the conditions before it runs the test.

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Past Papers

1
Exploring One-Variable Data
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- 1.1 Introducing Statistics: What Can We Learn from Data?
- 1.2 The Language of Variation: Variables
- 1.3 Representing a Categorical Variable with Tables
- 1.4 Representing a Categorical Variable with Graphs
- 1.5 Representing a Quantitative Variable with Graphs
- 1.6 Describing the Distribution of a Quantitative Variable
- 1.7 Summary Statistics for a Quantitative Variable
- 1.8 Graphical Representations of Summary Statistics
- 1.9 Comparing Distributions of a Quantitative Variable
- 1.10 The Normal Distribution
- 1.10 Practice
- 1.10 Answers
- 1.10 Exam tips
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2
Exploring Two-Variable Data
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- 2.1 Are Two Variables Related?
- 2.2 Two Categorical Variables
- 2.3 Comparing Groups with Conditional Distributions
- 2.4 Scatterplots for Two Quantitative Variables
- 2.5 Correlation
- 2.6 Linear Regression Models
- 2.7 Residuals
- 2.8 Least-Squares Regression and Its Fit
- 2.9 Departures from Linearity
- 2.9 Practice
- 2.9 Answers
- 2.9 Exam tips
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3
Collecting Data
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- 3.1 Can We Trust the Data We Collected?
- 3.2 Observational Studies and Experiments
- 3.3 Random Sampling
- 3.4 When Sampling Goes Wrong
- 3.5 Designing an Experiment
- 3.6 Choosing the Right Design
- 3.7 What an Experiment Lets You Conclude
- 3.7 The scope of a conclusion
- 3.7 Practice
- 3.7 Answers
- 3.7 Exam tips
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4
Probability, Random Variables, and Probability Distributions
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- 4.1 Random and Non-Random Patterns
- 4.2 Estimating Probabilities Using Simulation
- 4.3 Introduction to Probability
- 4.4 Mutually Exclusive Events
- 4.5 Conditional Probability
- 4.6 Independent Events and Unions of Events
- 4.7 Random Variables and Probability Distributions
- 4.8 Mean and Standard Deviation of Random Variables
- 4.9 Combining Random Variables
- 4.10 Introduction to the Binomial Distribution
- 4.11 Parameters for a Binomial Distribution
- 4.12 The Geometric Distribution
- 4.12 Practice
- 4.12 Answers
- 4.12 Exam tips
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5
Sampling Distributions
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- 5.1 Why Two Samples Never Match: Sampling Variability
- 5.2 The Normal Curve as a Model for a Statistic
- 5.3 The Central Limit Theorem
- 5.4 Good Guesses and Bad Guesses: Bias
- 5.5 The Sampling Distribution of a Sample Proportion
- 5.6 Comparing Two Groups: Difference of Sample Proportions
- 5.7 The Sampling Distribution of a Sample Mean
- 5.8 Comparing Two Groups: Difference of Sample Means
- 5.8 Practice
- 5.8 Answers
- 5.8 Exam tips
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6
Inference for Categorical Data: Proportions
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- 6.1 Why Be Normal?
- 6.2 Confidence Interval for a Proportion
- 6.3 Justifying a Claim from an Interval
- 6.4 Setting Up a Test for a Proportion
- 6.5 Interpreting p-Values
- 6.6 Concluding a Test
- 6.7 Type I and Type II Errors
- 6.8 Confidence Interval for a Difference of Proportions
- 6.9 Justifying a Claim About Two Proportions
- 6.10 Setting Up a Test for a Difference
- 6.11 Carrying Out a Test for a Difference
- 6.11 Practice
- 6.11 Answers
- 6.11 Exam tips
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7
Inference for Quantitative Data: Means
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- 7.1 Should I Worry About Error?
- 7.2 Confidence Interval for a Mean
- 7.3 Justifying a Claim About a Mean
- 7.4 Setting Up a Test for a Mean
- 7.5 Carrying Out a Test for a Mean
- 7.6 Confidence Interval for a Difference of Two Means
- 7.7 Justifying a Claim About Two Means
- 7.8 Setting Up a Test for a Difference of Means
- 7.9 Carrying Out a Test for a Difference of Means
- 7.10 Selecting and Communicating a Procedure
- 7.10 Practice
- 7.10 Answers
- 7.10 Exam tips
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8
Inference for Categorical Data: Chi-Square
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- 8.1 Are My Results Unexpected?
- 8.2 Setting Up a Goodness-of-Fit Test
- 8.3 Carrying Out a Goodness-of-Fit Test
- 8.4 Expected Counts in Two-Way Tables
- 8.5 Homogeneity or Independence?
- 8.6 Carrying Out a Test for Homogeneity or Independence
- 8.7 Choosing the Right Categorical Procedure
- 8.7 Practice
- 8.7 Answers
- 8.7 Exam tips
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9
Inference for Quantitative Data: Slopes
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- 9.1 Do Those Points Align?
- 9.2 Confidence Interval for a Slope
- 9.3 Justifying a Claim About a Slope
- 9.4 Setting Up a Test for a Slope
- 9.5 Carrying Out a Test for a Slope
- 9.5 Reading regression output
- 9.6 Selecting the Right Procedure
- 9.6 Practice
- 9.6 Answers
- 9.6 Exam tips
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