# Difference between revisions of "AP Statistics Curriculum 2007"

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===Outline=== | ===Outline=== | ||

− | + | This is an Internet-based E-Book for advance-placement (AP) statistics educational curriculum. The e-book is initially developed by the UCLA [[SOCR | 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. | * '''Motivation/Problem''': A real data set and fundamental challenge. | ||

* '''Approach''': Models & strategies for solving the problem, data understanding & inference. | * '''Approach''': Models & strategies for solving the problem, data understanding & inference. | ||

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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. | 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 ==== | + | ====[[AP_Statistics_Curriculum_2007_IntroUses |Uses and Abuses of Statistics]] ==== |

− | ====Design of Experiments ==== | + | ====[[AP_Statistics_Curriculum_2007_IntroDesign | Design of Experiments]] ==== |

− | ====Statistics with Calculators and Computers==== | + | ====[[AP_Statistics_Curriculum_2007_IntroTools |Statistics with Tools (Calculators and Computers)]]==== |

===Describing, Exploring, and Comparing Data=== | ===Describing, Exploring, and Comparing Data=== | ||

− | ====Summarizing data with Frequency Tables ==== | + | ====[[AP_Statistics_Curriculum_2007_EDA_Freq |Summarizing data with Frequency Tables ]]==== |

− | ====Pictures of Data ==== | + | ====[[AP_Statistics_Curriculum_2007_EDA_Pics |Pictures of Data]]] ==== |

− | ====Measures of Central Tendency ==== | + | ====[[AP_Statistics_Curriculum_2007_EDA_Center |Measures of Central Tendency]] ==== |

− | ====Measures of Variation ==== | + | ====[[AP_Statistics_Curriculum_2007_EDA_Var |Measures of Variation]] ==== |

− | ====Measures of | + | ====[[AP_Statistics_Curriculum_2007_EDA_Shape |Measures of Shape]]==== |

− | ====Exploratory Data Analysis ==== | + | ====[[AP_Statistics_Curriculum_2007_EDA_Plots | Graphs & Exploratory Data Analysis]] ==== |

===Probability=== | ===Probability=== | ||

− | ====Fundamentals==== | + | ====[[AP_Statistics_Curriculum_2007_Prob_Basics |Fundamentals]]==== |

− | ====Addition | + | ====[[AP_Statistics_Curriculum_2007_Prob_Rules |Addition & Multiplication Rules]] ==== |

− | + | ====[[AP_Statistics_Curriculum_2007_Prob_Simul |Probabilities Through Simulations]] ==== | |

− | ====Probabilities | + | ====[[AP_Statistics_Curriculum_2007_Prob_Count |Counting]] ==== |

− | ====Counting ==== | ||

===Probability Distributions=== | ===Probability Distributions=== | ||

− | ====Random Variables ==== | + | ====[[AP_Statistics_Curriculum_2007_Distrib_RV | Random Variables]] ==== |

− | ====Bernoulli & Binomial Experiments ==== | + | ====[[AP_Statistics_Curriculum_2007_Distrib_Binomial |Bernoulli & Binomial Experiments ==== |

− | ====Geometric, HyperGeometric & Negative Binomial==== | + | ====[[AP_Statistics_Curriculum_2007_Distrib_Dists |Geometric, HyperGeometric & Negative Binomial]]==== |

− | ==== | + | ====[[AP_Statistics_Curriculum_2007_Distrib_POisson |Poisson Distribution]]==== |

− | |||

===Normal Probability Distributions=== | ===Normal Probability Distributions=== | ||

− | ====The Standard Normal Distribution ==== | + | ====[[AP_Statistics_Curriculum_2007_Normal_Std |The Standard Normal Distribution]] ==== |

− | ====Nonstandard Normal Distribution: Finding Probabilities ==== | + | ====[[AP_Statistics_Curriculum_2007_Normal_Prob |Nonstandard Normal Distribution: Finding Probabilities]] ==== |

− | ====Nonstandard Normal Distributions: Finding Scores ==== | + | ====[[AP_Statistics_Curriculum_2007_Normal_Critical |Nonstandard Normal Distributions: Finding Scores (critical values)]] ==== |

===Relations Between Distributions=== | ===Relations Between Distributions=== | ||

− | ====The Central Limit Theorem ==== | + | ====[[AP_Statistics_Curriculum_2007_Limits_CLT |The Central Limit Theorem]] ==== |

− | ====Law of Large Numbers==== | + | ====[[AP_Statistics_Curriculum_2007_Limits_LLN |Law of Large Numbers]]==== |

− | ====Normal Distribution as Approximation to Binomial Distribution ==== | + | ====[[AP_Statistics_Curriculum_2007_Limits_Norm2Bin |Normal Distribution as Approximation to Binomial Distribution]] ==== |

− | ====Poisson Approximation to Binomial Distribution ==== | + | ====[[AP_Statistics_Curriculum_2007_Limits_Poisson2Bin |Poisson Approximation to Binomial Distribution]] ==== |

− | ====Binomial Approximation to HyperGeometric==== | + | ====[[AP_Statistics_Curriculum_2007_Limits_Bin2HyperG |Binomial Approximation to HyperGeometric]]==== |

− | ====Normal Approximation to Poisson==== | + | ====[[AP_Statistics_Curriculum_2007_Limits_Norm2Poisson |Normal Approximation to Poisson]]==== |

===Estimates and Sample Sizes=== | ===Estimates and Sample Sizes=== | ||

− | ====Estimating a Population Mean: Large Samples ==== | + | ====[[AP_Statistics_Curriculum_2007_Estim_L_Mean |Estimating a Population Mean: Large Samples]] ==== |

− | ====Estimating a Population Mean: Small Samples ==== | + | ====[[AP_Statistics_Curriculum_2007_Estim_S_Mean |Estimating a Population Mean: Small Samples]] ==== |

− | ====Estimating a Population Proportion ==== | + | ====[[AP_Statistics_Curriculum_2007_Estim_Proportion |Estimating a Population Proportion]] ==== |

− | ====Estimating a Population Variance==== | + | ====[[AP_Statistics_Curriculum_2007_Estim_Var |Estimating a Population Variance]]==== |

===Hypothesis Testing=== | ===Hypothesis Testing=== | ||

− | ====Fundamentals of Hypothesis Testing ==== | + | ====[[AP_Statistics_Curriculum_2007_Hypothesis_Basics |Fundamentals of Hypothesis Testing]] ==== |

− | ====Testing a Claim about a Mean: Large Samples ==== | + | ====[[AP_Statistics_Curriculum_2007_Hypothesis_L_Mean |Testing a Claim about a Mean: Large Samples]] ==== |

− | ====Testing a Claim about a Mean: Small Samples ==== | + | ====[[AP_Statistics_Curriculum_2007_Hypothesis_S_Mean |Testing a Claim about a Mean: Small Samples]] ==== |

− | ====Testing a Claim about a Proportion ==== | + | ====[[AP_Statistics_Curriculum_2007_Hypothesis_Proportion |Testing a Claim about a Proportion]] ==== |

− | ====Testing a Claim about a Standard Deviation or Variance==== | + | ====[[AP_Statistics_Curriculum_2007_Hypothesis_Var |Testing a Claim about a Standard Deviation or Variance]]==== |

===Inferences from Two Samples=== | ===Inferences from Two Samples=== | ||

− | ====Inferences about Two Means: Dependent Samples ==== | + | ====[[AP_Statistics_Curriculum_2007_Infer_2Means_Dep |Inferences about Two Means: Dependent Samples]] ==== |

− | ====Inferences about Two Means: Independent and Large Samples ==== | + | ====[[AP_Statistics_Curriculum_2007_Infer_2Means_Indep |Inferences about Two Means: Independent and Large Samples]] ==== |

− | ====Comparing Two Variances ==== | + | ====[[AP_Statistics_Curriculum_2007_Infer_BiVar |Comparing Two Variances]] ==== |

− | ====Inferences about Two Means: Independent and Small Samples==== | + | ====[[AP_Statistics_Curriculum_2007_Infer_2Means_S_Indep |Inferences about Two Means: Independent and Small Samples]]==== |

− | ====Inferences about Two Proportions ==== | + | ====[[AP_Statistics_Curriculum_2007_Infer_2Proportions |Inferences about Two Proportions]] ==== |

===Correlation and Regression=== | ===Correlation and Regression=== | ||

− | ====Correlation ==== | + | ====[[AP_Statistics_Curriculum_2007_GLM_Corr |Correlation]] ==== |

− | ====Regression ==== | + | ====[[AP_Statistics_Curriculum_2007_GLM_Regress |Regression]] ==== |

− | ====Variation and Prediction Intervals ==== | + | ====[[AP_Statistics_Curriculum_2007_GLM_Predict |Variation and Prediction Intervals]] ==== |

− | ====Multiple Regression ==== | + | ====[[AP_Statistics_Curriculum_2007_GLM_MultLin |Multiple Regression]] ==== |

===Multinomial Experiments and Contingency Tables=== | ===Multinomial Experiments and Contingency Tables=== | ||

− | ====Multinomial Experiments: Goodness-of-Fit ==== | + | ====[[AP_Statistics_Curriculum_2007_Contingency_Fit |Multinomial Experiments: Goodness-of-Fit]] ==== |

− | ====Contingency Tables: Independence and Homogeneity==== | + | ====[[AP_Statistics_Curriculum_2007_Contingency_Indep |Contingency Tables: Independence and Homogeneity]]==== |

===Statistical Process Control=== | ===Statistical Process Control=== | ||

− | ====Control Charts for Variation and Mean ==== | + | ====[[AP_Statistics_Curriculum_2007_Control_MeanVar |Control Charts for Variation and Mean]] ==== |

− | ====Control Charts for Attributes==== | + | ====[[AP_Statistics_Curriculum_2007_Control_Attrib |Control Charts for Attributes]]==== |

<hr> | <hr> |

## Revision as of 14:27, 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

#### Design of Experiments

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

### Describing, Exploring, and Comparing Data

#### Summarizing data with Frequency Tables

#### Pictures of Data]

#### Measures of Central Tendency

#### Measures of Variation

#### Measures of Shape

#### Graphs & Exploratory Data Analysis

### Probability

#### Fundamentals

#### Addition & Multiplication Rules

#### Probabilities Through Simulations

#### Counting

### Probability Distributions

#### Random Variables

#### [[AP_Statistics_Curriculum_2007_Distrib_Binomial |Bernoulli & Binomial Experiments

#### Geometric, HyperGeometric & Negative Binomial

#### Poisson Distribution

### Normal Probability Distributions

#### The Standard Normal Distribution

#### Nonstandard Normal Distribution: Finding Probabilities

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

### Relations Between Distributions

#### The Central Limit Theorem

#### Law of Large Numbers

#### Normal Distribution as Approximation to Binomial Distribution

#### Poisson Approximation to Binomial Distribution

#### Binomial Approximation to HyperGeometric

#### Normal Approximation to Poisson

### Estimates and Sample Sizes

#### Estimating a Population Mean: Large Samples

#### Estimating a Population Mean: Small Samples

#### Estimating a Population Proportion

#### Estimating a Population Variance

### Hypothesis Testing

#### Fundamentals of Hypothesis Testing

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

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

#### Testing a Claim about a Proportion

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

### Inferences from Two Samples

#### Inferences about Two Means: Dependent Samples

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

#### Comparing Two Variances

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

#### Inferences about Two Proportions

### Correlation and Regression

#### Correlation

#### Regression

#### Variation and Prediction Intervals

#### Multiple Regression

### Multinomial Experiments and Contingency Tables

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

#### Contingency Tables: Independence and Homogeneity

### Statistical Process Control

#### Control Charts for Variation and Mean

#### Control Charts for Attributes

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

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