Statistics
Daren Starnes


Course Description:


This course will focus on the content of the AP* Statistics course, with an emphasis on developing instructional strategies that help students master key statistical concepts and techniques.  We will discuss issues related to organizing and administering the course, such as student selection, resources, projects, assessment, and pacing.  Sessions devoted to AP* Exam preparation and grading will be incorporated throughout the week.  Considerable time will be devoted to learning how to use technology (TI-83/84/89 and computer software) to enhance student learning.


Course Objectives:


Participants will:

  1. Refine their understanding of statistical procedures and concepts in each of four major areas: exploratory data analysis, study design, probability and randomness, and statistical inference.
  2. Develop facility with using the TI-83/84/89 and computer software to manage, describe, analyze, and generate data.  Utilize technology to promote statistical thinking
  3. Craft instructional strategies for teaching AP* Statistics that take into account possible student misunderstandings, available technology, and the benefits of activity-based learning. Prepare for the AP* Audit.
  4. Learn how the AP* exam is graded, and use this information to prepare assessments for their own students that are holistic and rubric-based.

Preparing for the Course:


In order to get the most out of our time together, please do each of the following before you come to the first class meeting:

  1. Obtain a copy of the AP* Statistics Course Description and read it.  You can download this document from AP* Central (apcentral.collegeboard.com).
  2. Get the AP* Audit information for AP* Statistics and review it.  You can download this document from AP* Central (apcentral.collegeboard.com).
  3. Bring the textbook you will be using for the course if you have selected one.  If not, publishers will send free samples for you to examine.
  4. If you have taught the course before, please bring something that you have used to enhance student learning to share with the other members of the class. 

Daily Agenda


Day 1

Morning

Introductions, Welcome, Goals for the Week

Overview of AP* Statistics: a case study

Four themes: producing data, describing data, statistical models (probability & random variables), drawing conclusions from data (inference)

Planning your course: Materials, student selection, and the AP* Audit

Data Analysis Toolbox
    · Data—who, what, why, when, where, how, and by whom
    · Graphical displays—dotplots, boxplots, stemplots, histograms, ogives
    · Numerical summaries—measures of center and spread/variability; outliers
    · Statistical models—density curves
    · Interpretations in context

Afternoon

Exploratory Data Analysis

(1) Comparing distributions
(2) Transforming scores & effects on summary statistics
(3) Measures of relative standing—z-scores, percentiles
(4) Density curves and Normal distributions
TECHNOLOGY:
TI-83/84/89: Data entry, list management, Statistics Plots, One-Var Stats, Window Control
Standard computer output — descriptive statistics

Relationships between two quantitative variables

(1) Scatterplots and correlation
(2) Least-squares regression
(3) Assessing model quality: residuals and ; outliers and influential observations
TECHNOLOGY
TI-83/84/89: Scatterplots, LSRL, prediction, residual plots
Computer regression output



Day 2

Morning

Introduction to the AP* Exam

    · AP* exam structure and scoring
    · Grading session I

Producing data: the basics—Surveys, experiments, and observational studies

Designing Surveys, Observational Studies, and Experiments
    · Mastering technical vocabulary
    · Designing, conducting, and critiquing studies to enhance understanding

More on relationships between two variables

(1) Transforming to achieve linearity—power and logarithm transformations
(2) Relationships between categorical variables—marginal and conditional distributions
(3) Establishing causation (lurking variables, confounding, and common response)
TECHNOLOGY
TI-83/84/89: transformations and nonlinear models

Afternoon

Probability and simulation

(1)Designing simulations to estimate probabilities
(2) Probability rules: sample space, addition and multiplication, tree
diagrams, independence, conditional probability, tabular probability

Random Variables

(1) Discrete & continuous random variables
(2) Expected value and variance rules
(3) Binomial and Geometric random variables
TECHNOLOGY
TI-83/84/89: ProbSim APP; random variables; binomial and geometric probability


Day 3

Morning

Sampling distributions

(1) Sample Proportions: connection with the binomial distribution
(2) Sample Means and the Central Limit Theorem (CLT)
TECHNOLOGY:
Computer java applets

Estimating an unknown population parameter: confidence intervals

(1) Idea of a confidence interval and confidence level
(2) Inference Toolbox structure: parameters, conditions, calculations, interpretation
(3) Estimating a population mean: the t-distributions
(4) Estimating a population proportion; determining sample size
TECHNOLOGY:
Computer java applets
TI-83/84/89: Program CI2; confidence intervals

Afternoon

Testing a claim: significance testing

(1) The structure and logic of a significance test
(2) Inference Toolbox structure: hypotheses, conditions, calculations, interpretation
(3) Decision-making: Type I, II errors and Power
(4) Significance tests about a population mean (t-tests)
(5) Significance tests about a population proportion
TECHNOLOGY:
Computer java applets
TI-83/84/89: Program Type2; significance test procedures


Day 4

Morning

Comparing two population parameters

(1) Comparing two population means
    · Paired data versus independent samples
    · Confidence intervals
    · Significance tests
(2) Comparing two population proportions
    · Confidence intervals
    · Significance tests
TECHNOLOGY
Computer output for inference
TI-83/84/89: Two sample inference procedures

Afternoon

Inference about categorical data

Chi-square: goodness of fit, homogeneity of populations, tests of independence
TECHNOLOGY
Chi-square on the TI-83/84/89



Day 5

Regression Inference

Inference about the regression slope: confidence intervals and significance tests
TECHNOLOGY:
Computer regression output
TI-83/84/89: regression inference procedures

Exam preparation
    · Lessons learned from the AP* reading
    · Exam preparation strategies

Random raffle and graduation ceremony!


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