# AP Statistics Curriculum 2007

## Contents

- 1 This is an Outline of a General Advance-Placement (AP) Statistics Curriculum
- 1.1 Outline
- 1.2 Format
- 1.3 Introduction to Statistics
- 1.4 Describing, Exploring, and Comparing Data
- 1.5 Probability
- 1.6 Probability Distributions
- 1.7 Normal Probability Distributions
- 1.8 Relations Between Distributions
- 1.9 Estimates and Sample Sizes
- 1.10 Hypothesis Testing
- 1.11 Inferences from Two Samples
- 1.12 Correlation and Regression
- 1.13 Multinomial Experiments and Contingency Tables
- 1.14 Statistical Process Control

## This is an Outline of a General Advance-Placement (AP) Statistics Curriculum

### Outline

This is an Internet-based E-Book for advance-placement (AP) statistics educational curriculum. The e-book is initially developed by the UCLA Statistics Online Computational Resource (SOCR), however, any statistics instructor, researcher or educator is encouraged to contribute to this effort and improve the content of these learning materials.

### Format

Follow the instructions in this page to expand, revise or improve the materials in this e-book.

### Introduction to Statistics

#### The Nature of Data & Variation

No mater how controlled the environment, the protocol or the design, virtually any repeated measurement, observation, experiment, trial, study or survey is bound to generate data that varies because of intrinsic (internal to the system) or extrinsic (due to the ambient environment) effects. How many natural processes or phenomena in real life can we describe that have an exact mathematical closed-form description and are completely deterministic? How do we model the rest of the processes that are unpredictable and have random characteristics?

#### Uses and Abuses of Statistics

Statistics is the science of variation, randomness and chance. As such, statistics is different from other sciences, where the processes being studied obey exact deterministic mathematical laws. Statistics provides quantitative inference represented as long-time probability values, confidence or prediction intervals, odds, chances, etc., which may ultimately be subjected to varying interpretations. The phrase *Uses and Abuses of Statistics* refers to the notion that in some cases statistical results may be used as evidence to seemingly opposite theses. However, most of the time, common principles of logic allow us to disambiguate the obtained statistical inference.

#### Design of Experiments

Design of experiments is the blueprint for planning a study or experiment, performing the data collection protocol and controlling the study parameters for accuracy and consistency. Data, or information, is typically collected in regard to a specific process or phenomenon being studied to investigate the effects of some controlled variables (independent variables or predictors) on other observed measurements (responses or dependent variables). Both types of variables are associated with specific observational units (living beings, components, objects, materials, etc.)

#### Statistics with Tools (Calculators and Computers)

Overview TBD

### Describing, Exploring, and Comparing Data

#### Summarizing data with Frequency Tables

Overview TBD

#### Pictures of Data

Overview TBD

#### Measures of Central Tendency

Overview TBD

#### Measures of Variation

Overview TBD

#### Measures of Shape

Overview TBD

#### Graphs & Exploratory Data Analysis

### Probability

#### Fundamentals

Overview TBD

#### Addition & Multiplication Rules

Overview TBD

#### Probabilities Through Simulations

Overview TBD

#### Counting

Overview TBD

### Probability Distributions

#### Random Variables

Overview TBD

#### Bernoulli & Binomial Experiments

Overview TBD

#### Geometric, HyperGeometric & Negative Binomial

Overview TBD

#### Poisson Distribution

Overview TBD

### Normal Probability Distributions

#### The Standard Normal Distribution

Overview TBD

#### Nonstandard Normal Distribution: Finding Probabilities

Overview TBD

#### Nonstandard Normal Distributions: Finding Scores (critical values)

Overview TBD

### Relations Between Distributions

#### The Central Limit Theorem

Overview TBD

#### Law of Large Numbers

Overview TBD

#### Normal Distribution as Approximation to Binomial Distribution

Overview TBD

#### Poisson Approximation to Binomial Distribution

Overview TBD

#### Binomial Approximation to HyperGeometric

Overview TBD

#### Normal Approximation to Poisson

Overview TBD

### Estimates and Sample Sizes

#### Estimating a Population Mean: Large Samples

Overview TBD

#### Estimating a Population Mean: Small Samples

Overview TBD

#### Estimating a Population Proportion

Overview TBD

#### Estimating a Population Variance

Overview TBD

### Hypothesis Testing

#### Fundamentals of Hypothesis Testing

Overview TBD

#### Testing a Claim about a Mean: Large Samples

Overview TBD

#### Testing a Claim about a Mean: Small Samples

Overview TBD

#### Testing a Claim about a Proportion

Overview TBD

#### Testing a Claim about a Standard Deviation or Variance

Overview TBD

### Inferences from Two Samples

#### Inferences about Two Means: Dependent Samples

Overview TBD

#### Inferences about Two Means: Independent and Large Samples

Overview TBD

#### Comparing Two Variances

Overview TBD

#### Inferences about Two Means: Independent and Small Samples

Overview TBD

#### Inferences about Two Proportions

Overview TBD

### Correlation and Regression

#### Correlation

Overview TBD

#### Regression

Overview TBD

#### Variation and Prediction Intervals

Overview TBD

#### Multiple Regression

Overview TBD

### Multinomial Experiments and Contingency Tables

#### Multinomial Experiments: Goodness-of-Fit

Overview TBD

#### Contingency Tables: Independence and Homogeneity

Overview TBD

### Statistical Process Control

#### Control Charts for Variation and Mean

Overview TBD

#### Control Charts for Attributes

Overview TBD

- SOCR Home page: http://www.socr.ucla.edu

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