AP Statistics Curriculum 2007 IntroVar

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Contents

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

Outline

Each 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 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 Position

Exploratory Data Analysis

Probability

Fundamentals

Addition Rule

Multiplication Rule

Probabilities through Simulations

Counting

Probability Distributions

Random Variables

Bernoulli & Binomial Experiments

Geometric, HyperGeometric & Negative Binomial

Mean, Variance, and Standard Deviation for the Binomial Distribution

Poisson Distribution

Normal Probability Distributions

The Standard Normal Distribution

Nonstandard Normal Distribution: Finding Probabilities

Nonstandard Normal Distributions: Finding Scores

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




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