AP Statistics Curriculum 2007 Prob Basics

General Advance-Placement (AP) Statistics Curriculum - Fundamentals of Probability Theory

Fundamentals of Probability Theory

Probability theory plays role in all studies of natural processes across scientific disciplines. The need for a theoretical probabilistic foundation is obvious since natural variation effects all measurements, observations and findings about different phenomena. Probability theory provides the basic techniques for statistical inference.

Random Sampling

A simple random sample of n items is a sample in which every member of the population has an equal chance of being selected and the members of the sample are chosen independently.

• Example: Consider a class of students as the population under study. If we select a sample of size 5, each possible sample of size 5 must have the same chance of being selected. When a sample is chosen randomly it is the process of selection that is random. How could we randomly select five members from this class randomly? Random sampling from finite (or countable) populations is well-defined. On the contrary, random samplying of uncountable pupulations is only allowed under the Axiom of Choice.
• Questions:
• How would you go about randomly selecting five students from a class of 100?
• How representative of the population is the sample likely to be? The sample wont exactly resemble the population, there will be some chance variation. This discrepancy is called chance error due to sampling.
• Definition: Sampling bias is non-randomness that refers to some members having a tendency to be selected more readily than others. When the sample is biased the statistics turn out to be poor estimates.

Model Validation

Checking/affirming underlying assumptions.

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Examples

Computer simulations and real observed data.

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Hands-on activities

Step-by-step practice problems.

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