Cumulative Notes
AP Statistics
Prepared by: Earl L. Whitney, FSA, MAAA
Version 1.0
April 27, 2014
Copyright 2014, Earl Whitney, Reno NV. All Rights Reserved
, 2
AP Statistics Cumulative Notes
Table of Contents
Page Description
6 AP Statistics Formula Sheet
8 Part 1: Exploring Data
8 Variable Types
8 5‐Number Summary
8 Other Terms to Know
9 Frequency Distribution
9 Cumulative Frequency Distribution
10 Center, Shape and Spread
11 Types of Plots
13 Marginal Distributions
14 Normal Distribution
15 Part 2: Exploring Bivariate Data
15 Definitions
17 Formulas Relating to the Coefficient of Correlation of a Sample
18 Linear Combinations of Parameters and Statistics
19 Types of Regression Models
20 Chapter 10: Straightening Data In a Scatterplot
20 Selecting a Good Re‐Expression Model
22 Re‐Expression Models Based on the Scatterplot
23 Re‐Expression Models Based on the Residuals
24 Description of Individual Models
30 Chapter 12: Sample Surveys
30 Types of Samples
30 Types of Bias
31 Table of Key Statistics ad Parameters
31 The Valid Survey
32 Chapter 13: Experiments and Observational Studies
32 Observation Study
32 Experiment
32 Principles of Experimental Design
33 Diagramming an Experiment
33 Elements of an Experiment
33 Other Terms Relating to Experimentation
Version 1.0 April 27, 2014
, 3
AP Statistics Cumulative Notes
Table of Contents
Page Description
34 Part 4: Probability
34 Key Definitions
36 Geometric Probability Model
36 Binomial Probability Model
36 Normal Probability Model
37 Key Formulas
38 Chapter 18: Sampling Distribution Models
38 Central Limit Theorem
38 Key Assumptions
39 Symbols and Formulas for Proportions
39 Symbols and Formulas for Population Means
40 Chapter 19: Confidence Intervals for Proportions
40 Explaining a Confidence Interva'
40 Critical Values
40 Standard Deviation vs. Standard Error
40 Key Assumptions
41 Chapter 20: Hypothesis Testing for Proportions
41 Hypotheses
41 P‐Value
42 Four Steps of Hypothesis Testing
43 Z‐Values and P‐Values for Various Tests ‐ 95% Confidence
44 Chapter 21: More About Tests and Intervals
44 a‐Value
44 Rules for Rejecting H0
44 b‐Value
44 Power
44 Effect Size
45 95% Confidence Interval (When the Success/Failure Condition Fails)
45 Summary of p’s and n’s
46 Type I and Type II Errors
46 Interaction of a, b, and Power
47 Chapter 22: Comparing Two Proportions
47 Confidence Interval for the Difference of Two Proportions
47 Key Assumptions and Conditions
48 Hypothesis Testing
Version 1.0 April 27, 2014
, 4
AP Statistics Cumulative Notes
Table of Contents
Page Description
49 Chapter 23: Inferences About Means
49 Sample of Means
49 Confidence Interval for the Difference of Two Proportions
50 Using z vs. t
50 Key Assumptions and Conditions
50 Sample Size for a t‐Distribution
50 Special Considerations
50 Language for Confidence Intervals
51 Hypothesis Testing
51 Relationship Between Intervals and Tests
51 Finding the Required Sample Size
51 Finding the Required Sample Size ‐ Example
53 Chapter 24: Comparing Means
53 Boxplots
53 Sample of Means
53 Confidence Interval
54 Key Assumptions and Conditions
54 Sample Size for a t‐Distribution
54 Special Considerations
54 Hypothesis Testing
55 Pooled t‐Interval and t‐Test
56 Chapter 25: Inferences About Paired Data
56 Pairing
56 Sample of Means
56 Confidence Interval
57 Key Assumptions and Conditions
57 Hypothesis Testing
58 Statistical Inference Summary Chart
59 Chapter 26: Comparing Counts – The Distribution
59 Uses and Characteristics
59 Hypothesis tests
60 Testing Goodness of Fit
62 Testing Homogeneity or Independence
Version 1.0 April 27, 2014
AP Statistics
Prepared by: Earl L. Whitney, FSA, MAAA
Version 1.0
April 27, 2014
Copyright 2014, Earl Whitney, Reno NV. All Rights Reserved
, 2
AP Statistics Cumulative Notes
Table of Contents
Page Description
6 AP Statistics Formula Sheet
8 Part 1: Exploring Data
8 Variable Types
8 5‐Number Summary
8 Other Terms to Know
9 Frequency Distribution
9 Cumulative Frequency Distribution
10 Center, Shape and Spread
11 Types of Plots
13 Marginal Distributions
14 Normal Distribution
15 Part 2: Exploring Bivariate Data
15 Definitions
17 Formulas Relating to the Coefficient of Correlation of a Sample
18 Linear Combinations of Parameters and Statistics
19 Types of Regression Models
20 Chapter 10: Straightening Data In a Scatterplot
20 Selecting a Good Re‐Expression Model
22 Re‐Expression Models Based on the Scatterplot
23 Re‐Expression Models Based on the Residuals
24 Description of Individual Models
30 Chapter 12: Sample Surveys
30 Types of Samples
30 Types of Bias
31 Table of Key Statistics ad Parameters
31 The Valid Survey
32 Chapter 13: Experiments and Observational Studies
32 Observation Study
32 Experiment
32 Principles of Experimental Design
33 Diagramming an Experiment
33 Elements of an Experiment
33 Other Terms Relating to Experimentation
Version 1.0 April 27, 2014
, 3
AP Statistics Cumulative Notes
Table of Contents
Page Description
34 Part 4: Probability
34 Key Definitions
36 Geometric Probability Model
36 Binomial Probability Model
36 Normal Probability Model
37 Key Formulas
38 Chapter 18: Sampling Distribution Models
38 Central Limit Theorem
38 Key Assumptions
39 Symbols and Formulas for Proportions
39 Symbols and Formulas for Population Means
40 Chapter 19: Confidence Intervals for Proportions
40 Explaining a Confidence Interva'
40 Critical Values
40 Standard Deviation vs. Standard Error
40 Key Assumptions
41 Chapter 20: Hypothesis Testing for Proportions
41 Hypotheses
41 P‐Value
42 Four Steps of Hypothesis Testing
43 Z‐Values and P‐Values for Various Tests ‐ 95% Confidence
44 Chapter 21: More About Tests and Intervals
44 a‐Value
44 Rules for Rejecting H0
44 b‐Value
44 Power
44 Effect Size
45 95% Confidence Interval (When the Success/Failure Condition Fails)
45 Summary of p’s and n’s
46 Type I and Type II Errors
46 Interaction of a, b, and Power
47 Chapter 22: Comparing Two Proportions
47 Confidence Interval for the Difference of Two Proportions
47 Key Assumptions and Conditions
48 Hypothesis Testing
Version 1.0 April 27, 2014
, 4
AP Statistics Cumulative Notes
Table of Contents
Page Description
49 Chapter 23: Inferences About Means
49 Sample of Means
49 Confidence Interval for the Difference of Two Proportions
50 Using z vs. t
50 Key Assumptions and Conditions
50 Sample Size for a t‐Distribution
50 Special Considerations
50 Language for Confidence Intervals
51 Hypothesis Testing
51 Relationship Between Intervals and Tests
51 Finding the Required Sample Size
51 Finding the Required Sample Size ‐ Example
53 Chapter 24: Comparing Means
53 Boxplots
53 Sample of Means
53 Confidence Interval
54 Key Assumptions and Conditions
54 Sample Size for a t‐Distribution
54 Special Considerations
54 Hypothesis Testing
55 Pooled t‐Interval and t‐Test
56 Chapter 25: Inferences About Paired Data
56 Pairing
56 Sample of Means
56 Confidence Interval
57 Key Assumptions and Conditions
57 Hypothesis Testing
58 Statistical Inference Summary Chart
59 Chapter 26: Comparing Counts – The Distribution
59 Uses and Characteristics
59 Hypothesis tests
60 Testing Goodness of Fit
62 Testing Homogeneity or Independence
Version 1.0 April 27, 2014
