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## Revision as of 14:52, 14 June 2007

## Contents

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

Every topic discussed in the SOCR AP Curricumum should contain the following subsections:

**Motivation/Problem**: A real data set and fundamental challenge.**Approach**: Models & strategies for solving the problem, data understanding & inference.**Model Validation**: Checking/affirming underlying assumptions.**Computational Resources**: Internet-based SOCR Tools (including offline resources, e.g., tables).**Examples**: computer simulations and real observed data.**Hands-on activities**: Step-by-step practice problems.

### 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.

#### Uses and Abuses of Statistics

TBD

#### Design of Experiments

TBD

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

TBD

### Describing, Exploring, and Comparing Data

#### Summarizing data with Frequency Tables

TBD

#### Pictures of Data

TBD

#### Measures of Central Tendency

TBD

#### Measures of Variation

TBD

#### Measures of Shape

TBD

#### Graphs & Exploratory Data Analysis

### Probability

#### Fundamentals

TBD

#### Addition & Multiplication Rules

TBD

#### Probabilities Through Simulations

TBD

#### Counting

TBD

### Probability Distributions

#### Random Variables

TBD

#### Bernoulli & Binomial Experiments

TBD

#### Geometric, HyperGeometric & Negative Binomial

TBD

#### Poisson Distribution

TBD

### Normal Probability Distributions

#### The Standard Normal Distribution

TBD

#### Nonstandard Normal Distribution: Finding Probabilities

TBD

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

TBD

### Relations Between Distributions

#### The Central Limit Theorem

TBD

#### Law of Large Numbers

TBD

#### Normal Distribution as Approximation to Binomial Distribution

TBD

#### Poisson Approximation to Binomial Distribution

TBD

#### Binomial Approximation to HyperGeometric

TBD

#### Normal Approximation to Poisson

TBD

### Estimates and Sample Sizes

#### Estimating a Population Mean: Large Samples

TBD

#### Estimating a Population Mean: Small Samples

TBD

#### Estimating a Population Proportion

TBD

#### Estimating a Population Variance

TBD

### Hypothesis Testing

#### Fundamentals of Hypothesis Testing

TBD

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

TBD

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

TBD

#### Testing a Claim about a Proportion

TBD

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

TBD

### Inferences from Two Samples

#### Inferences about Two Means: Dependent Samples

TBD

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

TBD

#### Comparing Two Variances

TBD

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

TBD

#### Inferences about Two Proportions

TBD

### Correlation and Regression

#### Correlation

TBD

#### Regression

TBD

#### Variation and Prediction Intervals

TBD

#### Multiple Regression

TBD

### Multinomial Experiments and Contingency Tables

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

TBD

#### Contingency Tables: Independence and Homogeneity

TBD

### Statistical Process Control

#### Control Charts for Variation and Mean

TBD

#### Control Charts for Attributes

TBD

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

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