Cumulative Notes AP Statistics - MathGuy.US

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

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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

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April 27, 2014

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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

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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

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April 27, 2014

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AP Statistics Cumulative Notes Table of Contents

Page Description

65 Chapter 27: Inferences for Regression

65

Moel of the Idealized Line

65

Visualization

65

Key Assumptions and Conditions

66

Work Order

66

Calculations

67

Thoughts about the Size of the Standard Error

68

Hypothesis Tests and Confidence Intervals for Linear Regression on the TI-84

Version 1.0

April 27, 2014

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