Statistics

AP Statistics Summer Institute
Louisville, KY
July 21 – 24, 2015

In addition to hardcopies of activities done in the sessions, electronic copies and copies of all PowerPoints presentations will be shared.  Please bring a thumb drive so that I can download them for you.

Topics

General course information

Exploring Data

  • Part I: The many types of graphs, and which are applicable to the data at hand
  • Part II: Summary statistics, and how summary statistics are affected by arithmetic manipulations

Probability

  • Defining sample space, mutually exclusive events, exhaustive events, complements, dependent and independent events, conditional probability
  • Probability rules
  • A variety of probability questions and approaches
  • Discrete distribution probability calculations  (finite and infinite)
  • Normal probability calculations
  • Binomial probability calculations
  • Explanation of the conditions under which a binomial distribution can be approximated by a normal distribution
  • Probability simulations.
  • Probability as it relates to statistical tests

Linear regression

  • Do numbers give you the whole picture? What summary statistics may and may not reveal
  • Does r imply a value for r2 and vice versa?
  • Exploring the dangers of extrapolation
  • The significance of the “hat” in linear regression models
  • Linear transformations of bivariate data and their effects on summary statistics
  • Non-linear transformations of bivariate data: when, and how?
  • Residuals and their implication for linear regression models
  • Inference for regression
  • Association versus causation
  • Simpson’s paradox

Confidence intervals

  • Investigating the “confidence” in confidence intervals
  • PANIC isn’t something to be avoided when it comes to confidence intervals
  • Confidence intervals for a population mean (unrealistic, and realistic)
  • Confidence intervals for a population proportion
  • Confidence intervals for the slope of a regression line
  • Confidence intervals for the difference if two population means
  • Confidence intervals for the difference of two population proportions

Hypothesis testing

  • Understanding the basic principles behind hypothesis testing
  • Forming the null and alternative hypotheses
  • Random sampling and its positive effect on results for hypothesis tests
  • Inference regarding means
  • Inference regarding proportions
  • The PHANTOMS process for hypothesis testing
  • Hypothesis tests for a population mean
  • Hypothesis tests for a population proportion
  • Hypothesis tests for regression
  • Hypothesis tests for the difference of two population means
  • Hypothesis tests for the difference of two population proportions
  • Hypothesis tests for categorical data: Chi-square GOF and two-way tests
  • Inference for Chi-square tests
  • Chi-square test residuals

Investigations

  • Investigating randomness
  • Investigating irrational numbers
  • Investigating whether change has occurred
  • Technology other than the graphing calculator (no investment of funds needed!)
  • Why every student should study Statistics

I will follow the topics sequentially as they are listed.  Timing depends on the audience, but, if time remains, I’ll recap the Summer 2015 free response questions.  (I am a reader of the exam.)