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AP Statistics

Flashcards • Study notes
1.1.1 Questions, Context, and Variation in Data
1.2.1 Identifying Variables in a Data Set
1.2.1 Identifying Variables in a Data Set
1.2.3 Quantitative Variables
1.3.1 Frequency Tables for Categorical Data
1.3.2 Relative Frequency Tables and Proportions
1.3.3 Describing Categorical Data in Context
1.4.1 Bar Graphs for Categorical Data
1.4.2 Interpreting Bar Height and Bar Length
1.4.3 Other Graphs for Categorical Data
1.4.4 Making Claims from Categorical Graphs
1.4.5 Comparing Categorical Data Sets
1.5.1 Discrete and Continuous Quantitative Variables
1.5.2 Histograms and Interval Widths
1.5.3 Stem-and-Leaf Plots
1.5.4 Dotplots for Individual Observations
1.5.5 Cumulative Graphs and Other Quantitative Displays
1.6.1 Shape, Center, Spread, and Unusual Features
1.6.2 Outliers in One-Variable Data
1.6.3 Skewed and Symmetric Distributions
1.6.4 Peaks, Modality, and Uniform Distributions
1.6.5 Gaps and Clusters
1.6.6 Descriptive Statistics and Conjectures
1.7.1 Statistics and the Mean
1.7.2 Median, Quartiles, and Percentiles
1.7.3 Range and Interquartile Range
1.7.4 Standard Deviation and Variance
1.7.5 Changing Units and Detecting Outliers
1.7.6 Choosing Resistant and Nonresistant Measures
1.8.1 The Five-Number Summary
1.8.2 Boxplots and Outliers
1.8.3 Using Summary Statistics to Justify Claims
1.8.4 Mean and Median in Skewed Distributions
1.9.1 Comparing Quantitative Graphs
1.9.2 Comparing Numerical Summaries
1.10.1 Parameters and Normal Distribution Models
1.10.2 Shape, Mean, and Standard Deviation of Normal Curves
1.10.3 The Empirical Rule
1.10.4 Standardized Scores and z-Scores
1.10.5 Normal Proportions, Percentiles, and Technology
1.10.6 Comparing Relative Position with Percentiles and z-Scores
2.1.1 Investigating Possible Relationships in Data
2.2.1 Bar Graphs for Two Categorical Variables
2.2.2 Comparing Distributions and Associations from Graphs
2.2.3 Two-Way Tables and Joint Relative Frequency
2.3.1 Marginal Relative Frequencies
2.3.2 Conditional Relative Frequencies
2.3.3 Comparing Statistics for Categorical Variables
2.4.1 Bivariate Quantitative Data and Scatterplots
2.4.2 Explanatory and Response Variables
2.4.3 Direction of Association in Scatterplots
2.4.4 Form and Strength of Association
2.4.5 Unusual Features in Scatterplots
2.5.1 Calculating and Understanding Correlation
2.5.2 Interpreting the Correlation Coefficient
2.5.3 Correlation
2.6.1 Using Linear Regression to Predict Responses
2.6.2 Calculating Predicted Values
2.6.3 Extrapolation and Prediction Reliability
2.7.1 Calculating and Plotting Residuals
2.7.2 Using Residual Plots to Assess Models
2.8.1 The Least-Squares Regression Line
2.8.2 Slope
2.8.3 Coefficient of Determination
2.8.4 Interpreting Regression Coefficients
2.9.1 Outliers in Regression
2.9.2 High-Leverage and Influential Points
2.9.3 Transforming Data to Improve Linearity
2.9.4 Evaluating Transformed Regression Models
3.1.1 Trustworthy Data Collection Methods
3.2.1 Populations and Samples
3.2.2 Observational Studies and Sample Surveys
3.2.3 Experiments and Assigned Treatments
3.2.4 Generalizing and Determining Causation
3.3.1 Simple Random Samples and Replacement
3.3.2 Stratified Random Samples
3.3.3 Cluster Samples
3.3.4 Systematic Samples and Censuses
3.3.5 Choosing an Appropriate Sampling Method
3.4.1 Understanding Bias in Sampling
3.4.2 Voluntary Response Bias
3.4.3 Undercoverage Bias
3.4.4 Nonresponse Bias
3.4.5 Response Bias and Non-Random Sampling
3.5.1 Experimental Units, Factors, Treatments, and Responses
3.5.2 Confounding Variables in Experiments
3.5.3 Elements of a Well-Designed Experiment
3.5.4 Completely Randomized Designs
3.5.5 Blinding, Control Groups, and Placebos
3.5.6 Randomized Blocks and Matched Pairs
3.6.1 Matching Experimental Designs to Situations
3.7.1 Statistical Inference and Experimental Results
3.7.2 Random Assignment and Statistical Significance
3.7.3 Causation and Generalizing Experimental Results
4.1.1 Recognising Patterns in Data
4.1.2 Deciding Whether Patterns Could Be Random
4.2.1 Random Processes, Trials, and Outcomes
4.2.2 Events as Collections of Outcomes
4.2.3 Building a Simulation Model
4.2.4 Estimating Probability from Repeated Trials
4.3.1 Sample Spaces and Equally Likely Outcomes
4.3.2 Probability Values and Complements
4.3.3 Interpreting Probability in the Long Run
4.4.1 Understanding Joint Probability
4.4.2 Identifying Mutually Exclusive Events
4.5.1 Calculating Conditional Probability
4.5.2 Using the General Multiplication Rule
4.6.1 Deciding Whether Events Are Independent
4.6.2 Probability Rules for Independent Events
4.6.3 Calculating the Union of Two Events
4.7.1 Defining Random Variables
4.7.2 Discrete Random Variables
4.7.3 Representing Probability Distributions
4.7.4 Cumulative Distributions and Interpretation
4.8.1 Parameters of Discrete Random Variables
4.8.2 Calculating Mean and Standard Deviation
4.8.3 Interpreting Parameters in Context
4.9.1 Means of Linear Combinations
4.9.2 Independence and Variance of Combinations
4.9.3 Effects of Linear Transformations
4.10.1 Constructing Binomial Distributions
4.10.2 Conditions for a Binomial Random Variable
4.10.3 Calculating Binomial Probabilities
4.11.1 Mean and Standard Deviation of a Binomial Variable
4.11.2 Interpreting Binomial Probabilities and Parameters
4.12.1 Conditions for a Geometric Random Variable
4.12.2 Calculating Geometric Probabilities
4.12.3 Mean, Standard Deviation, and Interpretation
5.1.1 Explaining Variation Between Samples
5.1.2 Random and Non-Random Sample Differences
5.2.1 Continuous Random Variables and Normal Models
5.2.2 Finding Normal Probabilities from Area
5.2.3 Finding Intervals from Normal Areas
5.2.4 Using Normal Distributions as Approximations
5.3.1 What a Sampling Distribution Represents
5.3.2 The Central Limit Theorem for Sample Means
5.3.3 Conditions for Applying the Central Limit Theorem
5.3.4 Simulating Sampling and Randomization Distributions
5.4.1 Understanding Unbiased Estimators
5.4.2 Point Estimates and Estimator Variability
5.5.1 Mean and Standard Deviation of Sample Proportions
5.5.2 The 10% Rule for Sample Proportions
5.5.3 Normal Conditions for Sample Proportions
5.5.4 Interpreting Sample Proportion Distributions
5.6.1 Mean and Standard Deviation for Difference in Proportions
5.6.2 The 10% Rule for Difference in Proportions
5.6.3 Normal Conditions for Difference in Proportions
5.6.4 Interpreting Difference in Proportions Distributions
5.7.1 Mean and Standard Deviation of Sample Means
5.7.2 The 10% Rule for Sample Means
5.7.3 Normal Conditions for Sample Means
5.7.4 Interpreting Sample Mean Distributions
5.8.1 Mean and Standard Deviation for Difference in Means
5.8.2 The 10% Rule for Difference in Means
5.8.3 Normal Conditions for Difference in Means
5.8.4 Interpreting Difference in Means Distributions
6.1.1 Random and Non-Random Variation in Sample Distributions
6.2.1 Choosing a One-Sample z-Interval for a Proportion
6.2.2 Checking Independence for a One-Proportion Interval
6.2.3 Checking Normality for a One-Proportion Interval
6.2.4 Standard Error, Critical Values, and Margin of Error
6.2.5 Planning Sample Size for a Desired Margin of Error
6.2.6 Calculating and Using a Confidence Interval for a Proportion
6.3.1 Interpreting a Confidence Interval for a Population Proportion
6.3.2 Understanding Confidence Level Through Repeated Sampling
6.3.3 Writing Interval Interpretations in Context
6.3.4 Using a Confidence Interval to Support a Claim
6.3.5 How Sample Size and Confidence Level Affect Width
6.3.6 Connecting Margin of Error and Interval Width
6.4.1 Writing Null and Alternative Hypotheses for One Proportion
6.4.2 Choosing the Direction of the Alternative Hypothesis
6.4.3 Stating Hypotheses Using Population Proportion Notation
6.4.4 Choosing a One-Sample z-Test for a Proportion
6.4.5 Checking Conditions for a One-Proportion Test
6.4.6 Using the Null Value to Check Normality
6.5.1 Understanding the Null Distribution for a Test
6.5.2 Calculating a z-Statistic for One Proportion
6.5.3 Finding a p-Value from the Test Statistic
6.5.4 Interpreting One-Sided and Two-Sided p-Values
6.5.5 Interpreting a p-Value in Context
6.6.1 Understanding the Significance Level
6.6.2 Making a Formal Decision with a p-Value
6.6.3 Connecting Decisions to Evidence for the Alternative
6.6.4 Writing Conclusions in Context
6.6.5 Avoiding Incorrect Conclusions About the Null
6.6.6 Judging the Strength of Evidence from p-Values
6.7.1 Identifying Type I and Type II Errors
6.7.2 Connecting Alpha to the Probability of Type I Error
6.7.3 Understanding Power and Type II Error
6.7.4 Factors That Reduce the Probability of Type II Error
6.7.5 Interpreting Consequences of Testing Errors
6.7.6 Choosing Alpha Based on Error Consequences
6.8.1 Choosing a Two-Sample z-Interval for Two Proportions
6.8.2 Checking Independence for Two-Proportion Intervals
6.8.3 Checking Normality for Two-Proportion Intervals
6.8.4 Calculating a Confidence Interval for a Difference in Proportions
6.8.5 Using Two-Proportion Intervals to Find Estimates with Units
6.9.1 Interpreting Confidence Level for a Difference of Proportions
6.9.2 Writing Two-Proportion Interval Interpretations in Context
6.9.3 Using a Two-Proportion Interval to Justify a Claim
6.10.1 Writing Hypotheses for a Difference of Two Proportions
6.10.2 Choosing the Direction of a Two-Proportion Alternative
6.10.3 Choosing a Two-Sample z-Test for Two Proportions
6.10.4 Checking Independence for a Two-Proportion Test
6.10.5 Using the Pooled Proportion to Check Normality
6.11.1 Calculating the Two-Proportion z-Statistic
6.11.2 Interpreting the p-Value for Two Proportions
6.11.3 Making a Decision for a Two-Proportion Test
6.11.4 Using Test Results to Answer the Research Question
7.1.1 Random Variation and Inference Errors
7.1.2 Questions Raised by Possible Errors
7.2.1 Understanding the t-Distribution
7.2.2 Degrees of Freedom and t-Distributions
7.2.3 Choosing a One-Sample t-Interval
7.2.4 Confidence Intervals for Matched Pairs
7.2.5 Checking Conditions for a One-Sample t-Interval
7.2.6 Calculating a One-Sample t-Interval
7.3.1 Interpreting a Confidence Interval for a Mean
7.3.2 Writing Confidence Statements in Context
7.3.3 Using an Interval to Support a Claim
7.3.4 Sample Size, Confidence Level, and Interval Width
7.4.1 Choosing a One-Sample t-Test
7.4.2 Setting Up Tests for Matched Pairs
7.4.3 Writing Hypotheses for a Population Mean
7.4.4 Defining Differences in Matched Pairs
7.4.5 Checking Conditions for a One-Sample t-Test
7.5.1 Calculating the One-Sample t-Statistic
7.5.2 Finding and Interpreting a p-Value
7.5.3 Making a Formal Test Decision
7.5.4 Justifying a Claim in Context
7.6.1 Sampling Distribution for the Difference of Means
7.6.2 Choosing a Two-Sample t-Interval
7.6.3 Checking Conditions for a Two-Sample t-Interval
7.6.4 Margin of Error and Standard Error for Two Means
7.6.5 Calculating a Two-Sample t-Interval
7.7.1 Interpreting a Confidence Interval for Two Means
7.7.2 Context for Samples and Populations
7.7.3 Using an Interval to Compare Two Means
7.7.4 Sample Size and Interval Width for Two Means
7.8.1 Choosing a Two-Sample t-Test
7.8.2 Writing Hypotheses for Two Means
7.8.3 Choosing One-Sided or Two-Sided Alternatives
7.8.4 Checking Conditions for Two-Sample Tests
7.9.1 Calculating the Two-Sample t-Statistic
7.9.2 Degrees of Freedom and Technology
7.9.3 Interpreting a p-Value for Two Means
7.9.4 Making and Justifying a Decision
7.10.1 Selecting the Correct Inference Procedure
7.10.2 Implementing Inference Procedures Correctly
7.10.3 Communicating Statistical Inference
8.1.1 Observed and Expected Counts in Categorical Data
8.1.2 Random and Non-Random Variation in Results
8.2.1 Expected Counts and the Null Hypothesis
8.2.2 Measuring Distance with the Chi-Square Statistic
8.2.3 Shape of the Chi-Square Distribution
8.2.4 Hypotheses for a Goodness-of-Fit Test
8.2.5 Choosing and Calculating for Goodness of Fit
8.2.6 Conditions for a Chi-Square Goodness-of-Fit Test
8.3.1 Calculating the Goodness-of-Fit Test Statistic
8.3.2 Degrees of Freedom and the Null Distribution
8.3.3 Finding the P-Value for Goodness of Fit
8.3.4 Interpreting the Goodness-of-Fit P-Value
8.3.5 Making a Decision with the Significance Level
8.3.6 Justifying a Population Claim from Test Results
8.4.1 Marginal Totals in Two-Way Tables
8.4.2 Calculating Cell Expected Counts
8.5.1 Hypotheses for Homogeneity Tests
8.5.2 Hypotheses for Independence Tests
8.5.3 Choosing a Chi-Square Test for Homogeneity
8.5.4 Choosing a Chi-Square Test for Independence
8.5.5 Randomness and Independence Conditions for Two-Way Tables
8.5.6 Large Counts Condition for Two-Way Table Tests
8.6.1 Calculating the Two-Way Table Chi-Square Statistic
8.6.2 Degrees of Freedom for Homogeneity and Independence
8.6.3 Finding and Understanding the P-Value
8.6.4 Interpreting a P-Value in Context
8.6.5 Rejecting or Failing to Reject the Null Hypothesis
8.6.6 Justifying Claims About Populations or Associations
8.7.1 Comparing Inference Procedures for Categorical Data
8.7.2 Matching Research Questions to Chi-Square Tests
8.7.3 Applying Categorical Inference Learning Objectives
9.1.1 Random and Non-Random Variation Around a Line
9.2.1 Sample and Population Regression Lines
9.2.2 Residuals and the Standard Deviation of Residuals
9.2.3 Sampling Distribution and Standard Error of the Slope
9.2.4 Choosing a t-Interval for a Regression Slope
9.2.5 Checking Conditions for a Slope Confidence Interval
9.2.6 Constructing the Confidence Interval for Slope
9.3.1 Interpreting a Confidence Interval for Slope
9.3.2 Referring to the Sample and Population in Context
9.3.3 Using an Interval to Support or Refute a Claim
9.3.4 How Sample Size Affects Interval Width
9.4.1 Choosing a t-Test for a Regression Slope
9.4.2 Writing Hypotheses for a Slope Test
9.4.3 Checking Linearity and Equal Variation
9.4.4 Checking Independence and Normality for Testing
9.5.1 The Null Distribution for a Slope Test
9.5.2 Calculating the Test Statistic for Slope
9.5.3 Interpreting the p-Value in Context
9.5.4 Making a Formal Decision About the Slope
9.5.5 Using Test Results to Answer a Research Question
9.6.1 Selecting the Right Inference Procedure
9.6.2 Applying Inference Objectives Across Contexts

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