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.)