# Teaching AP Statistics Part II: Inferential Statistics

Welcome to Math Teacher Link Module 6 Part II. This is a web-based, technology-intensive course for in-service teachers wishing to update and/or review topics in descriptive statistics for AP Statistics courses at the high school level. The objective of this course module is to aid high school educators in teaching the second semester of a full year course of AP Statistics. Together with the companion course Module 6 Part I, these two courses provide the necessary background in statistics to teach a full-year high school course in AP Statistics.

The primary focus is teaching statistics and improving the quality of instruction by using assistive technology. Both the content of statistics and effective instructional strategies reflect the NCTM Standards for curriculum and for teaching and the College Board AP Statistics course description.

This module is composed of the following eight units:

• Unit 1: Introduction and Teacher's Perspective
• Unit 2: Central Limit Theorem
• Unit 3: Estimates (Confidence Intervals)
• Unit 4: Hypothesis Testing with One Sample
• Unit 5: Hypothesis Testing with Two Samples
• Unit 6: Tests of Correlation and Regression
• Unit 7: Multinomial Experiments; Contingency Tables
• Unit 8: ANOVA

Enrollees will complete one unit at a time, but must complete all eight units to earn credit for this module.

The units are written purposely brief, allowing the enrollee to research and self-study unfamiliar topics in depth, and minimize time spent on understood topics. Enrollees are expected to do a significant amount of independent study to complete this course.

Content Pre-requisite: It is assumed that enrollees have completed Math 490 Module 6 Part I and/or have a good understanding of probability and probability distributions (binomial, normal, student t, Chi-square), and of statistic fundamentals (descriptive statistics).

Common Core Standards for Mathemtical Practice that are emphasized include:

• 1. Make sense of problems and persevere in solving them.
• 3. Construct viable arguments.
• 4. Model with mathematics.
• 5. Use appropriate tools strategically.
• 6. Attend to precision.

Teaching AP Statistics Part II: Inferential Statistics was written by Carol Castellon of the University of Illinois Department of Mathematics. The original course, "Teaching Statistics in the High School", was written by Ken Travers and Jeremy Bartusch, revised in 2002 by Amy Trefzger.

# Detailed Description

This is the second module of a technology intensive, networked-based, two module course in the fundamentals of probability and statistics. These modules provide the necessary background for teachers of high school statistics to teach a full year of AP Statistics. Module 6 Part II deals with inferential statistics including Central Limit Theorem, confidence intervals, hypothesis testing, and ANOVA.

The outline of these modules is closely linked to the AP Program Topic Outline and the Supplement Text (AMSCO). As a result, be aware that the outline of our Module may not coincide exactly with your high school's text. The general pattern for taking the module will consist of reading the book in hard copy and doing exercises using software introduced in the Units. In most cases, the exercises can be done with a graphing calculator such as the TI-83+. Exercises and other activities will be conducted in electronic format and submitted to the instructor via the Internet.

Unit 1: Introduction and Teacher's Perspective
In this unit, participants will be introduced to sampling and sampling distributions.

Unit 2: Central Limit Theorem
Unit 2 discusses the Central Limit Theorem using the software Resampling StatsTM.

Unit 3: Estimates (Confidence Intervals)
Unit 3 covers point and interval estimates, or confidence intervals, and the software StatDiskTM.

Unit 4: Hypothesis Testing with One Sample
Unit 4 looks at traditional hypothesis tests with one sample using the software MinitabTM.

Unit 5: Hypothesis Testing with Two Samples
Unit 5 expands the discussion to hypothesis tests with both independent and dependent samples.

Unit 6: Tests of Correlation and Regression
Unit 6 looks at correlation and regression using the software FathomTM.

Unit 7: Multinomial tests; Contingency Tables
Unit 7 gives participants a chance to explore multinomial tests, using a variety of software applications.

Unit 8: ANOVA
Unit 8 focuses on Analysis of Variance, using the software JMPTM, or a new application of your choice.

AttachmentSize
Mod6B-1.doc43 KB
Mod6B-2.doc34 KB
Intro_to_R.pdf232.74 KB
Mod6B-3.doc34 KB
Mod6B-4.doc54 KB
Mod6B-5.doc51.5 KB
Mod6B-6.doc61.5 KB
Mod6B-7.doc45 KB
Mod6B-8.doc59.5 KB

# Required Materials

In addition to the general requirements for participating in Math Teacher Link, this module also has the following requirements:

Supplement Text
Regardless of which textbook you will be using in your classroom, this text offers an excellent supplement to any AP Statistics course.

• AP Statistics: Preparing for the AP Exam, Bohan, AMSCO 2000, ISBN: 1-56765-527-0

Primary Text
Since the AMSCO text is only a supplement and not meant as a stand-alone textbook, this course also requires an AP Statistics recommended primary text. Such texts include, but are not limited to:

• Elementary Statistics 8/e, Triola, Addison Wesley 2001, ISBN 0-201-61480-4
• Elementary Statistics Update 9/e, Triola, Addison Wesley 2005, ISBN: 0-321-28839-4
• Elementary Statistics 6/e, Weiss, Addison Wesley 2005, ISBN:0-201-77130-6
• Elementary Statistics 2/e, Bluman, McGraw Hill 2003, ISBN: 0-07-256042-8
• Statistics and Data Analysis 2/e, Peck/Olsen/Devore, Thompson 2005, ISBN: 0-534-46710-5
• Understandable Statistics 7/e, Brase, Houghton Mifflin 2003, ISBN: 0-618-26509-0

Please consult with Math Teacher Link if you would like to use a Primary Text not on the above list. A free trial copy of high school textbooks is often granted to interested teachers. Contact the publishers above to inquire about such a request.

Software
Enrollees will also need to use several types of statistical software in this course. If the participant or participant's school does not own a license for license for own of these brands, each software package offers a 30-day free trial version that can be downloaded from the internet. After downloading the software package, the enrollee should plan to complete the Unit within the 30-day trial period provided by the downloaded software. A goal of this course is to introduce a variety of software and demonstrate possible applications of the software; the enrollee can then decide whether the software is appropriate for their own school setting. Software packages include:

Calculator
Enrollees are required to use a graphing calculator with built-in statistics tests; any graphing calculator approved for the AP test is suitable for this course. The course instructor will assume use of a TI-83 Plus.

Optional Video
There are several commercial videos that may help high school students in understanding statistical concepts. An older yet excellent series is "Against All Odds: Inside Statistics," an Annenberg/CPB series.
http://www.learner.org/catalog/series65.html

# Step By Step

We estimate that the work that you will do for each unit in this module will take about 20 hours to complete. You can do the work at school or at home, and you can fit it into your schedule however you see fit. We recommend that you set aside some time, about ten hours each week, to work on the module. This should enable you to finish each unit within 2 weeks from the time that you start.

# Step #1 Knowing Your Classroom

We want you to practice and be comfortable working with a text that you will in turn use with your students. Yet, Math Teacher Link realizes that while this Module may provide you with new resources and ideas, you may be bound to use textbooks others than those recommended here.
• Become familiar with the contents of your high school's Statistics textbook if you have not already done so. Also obtain any supplementary materials your school has available which may include the following.
• Teacher's Edition of the text
• Solutions Manual
• Publisher Provided Software and Manual
This is a course in teaching statistics, so an appropriate level of statistical understanding and proficiency should already exist. If not, please refresh your own skills at the outset or as the course moves from topic to topic.
• Become familiar with the various technology formats available to students at your high school. We know that the extent of resources varies from school to school, but as the AP Program has a certain expectation of assistive technology, as too do we. More on this can be read in the AP Statistics Course Description under "The Use of Technology." The URL link to the Course Description appears in Step 2.

# Step #2 New Resources

In our goal to become better teachers, we must have outlets to other teachers and resources to improve our own skills.
• Register on the official website of College Board, the governing organization of the Advanced Placement program. We will occasionally be downloading resources and reading articles posted on their website. They also have an excellent resource known as the AP Statistics Electronic Discussion Group (EDG) which allows you share ideas with fellow teachers.
• Access the AP Statistics Course Home Page on that site and download the most recent version of the AP Statistics Course Description to be read. The Course Description includes many descriptions of AP Program including the Topic Outline which will guide us through the Units in this Module.

This is a link to the 2005-2006 version. http://apcentral.collegeboard.com/repository/statistics_cd_0506_4328.pdf

• Familiarize yourself as to what the NCTM standards say regarding statistics and probability instruction at various grade levels. The NCTM Standards are broken down into different grade levels: Pre-K-2, 3-5, 6-8, and 9-12. Pay particular attention to the 9-12 grade level and read those standards with respect to statistics and probability instruction.
• Another excellent resource for teachers to communicate is the Statistics Teacher Network. Published by the American Statistical Association and the National Council of Teachers of Mathematics, this free newsletter contains teaching ideas and activities for all grades. You may sign up for a newsletter to be delivered to you, or you can just peruse the articles online.

http://www.amstat.org/education/stn/ Write to Statistics Teacher Network, c/o American Statistical Association, 1429 Duke St, Alexandria, VA 22314-3415, or send an email to madge@amstat.org to subscribe for a delivered newsletter.

• Browse through the Office for Mathematics, Science, and Technology Education (MSTE) Web Site. The MSTE site contains a variety of information and is an excellent resource for educators at any level. Participants should start by looking at the MSTE Data Archives which contains data sets that are available for you to use in your classroom. Next take some time to look at the interactive statistics assignments available. Notice that in addition to statistics lessons, there are also lessons for other math and science classes.

MSTE homepage: http://www.mste.uiuc.edu
Data Archives: http://www.mste.uiuc.edu/malcz/data/archive.html
Lessons and Curriculum: http://www.mste.uiuc.edu/html.f/resource.php

• The homework exercises we've created provide you the opportunity to try a variety of educational journals and websites for references to other such programs. Many companies offer free trial periods while you test their software. There are also many programs available to use directly on the internet using JAVA applications. The following website may be helpful in your search:

# Step #3 Unit 1: Reading, Review, and Exercises

Download Unit 1 using the hyperlink on the Detailed Description page. Open the file Mod6B-1.doc in Microsoft Word. This file contains a reading assignment from the course texts, some summary definitions and examples for review, and required exercise assignments.

Reading assignments appear in italic magenta. Enrollees are required to read assigned pages from the AMSCO text and self-test using the review exercises provided in the AMSCO text. While we do provide a review of some of the more important topics, it is assumed that enrollees will do a significant amount of independent study on all statistics topics to be best prepared for teaching.

Exercise assignments appear in red text surrounded by a red border. These should be completed and properly labeled in a new Microsoft Word document. Some responses may require a screenshot of the output from one of the software programs. If the problem involves using your graphing calculator, you need to download screenshots of your work using the GraphLink. Answers to open-ended questions may be as brief or lengthy as you deem necessary to fully explain.

If a Unit requires downloading a free trial of a software package, you should plan to complete the Unit and submit the assignment within the 30-day trial period.

Completed exercise assignments are to be submitted electronically by going to the Moodle Hand In system at http://go.illinois.edu/NetMathMTL6b. The login to the Moodle Hand In system is the NetID you obtained through the CITES claiming site. The Enrollment Key to get into the Moodle is: NetMathMTL6b.

# Step #4 Feedback on Unit 1

After submitting your completed work from Unit 1, the course instructor will review and grade your assignment within a few days. The course instructor will post comments and feedback regarding your exercises, lesson, and exam questions in the Word documents that you submitted. These updated files will then be posted in the Moodle Hand-In system. Download the graded files, and review the course instructor's comments.

# Step #5 Units 2-8

Download the file Mod6B-2.doc in Microsoft Word. This file contains a reading assignment from the course texts, some summary definitions and examples for review, and required exercise assignments just as in Unit 1. Complete the exercise assignments for Unit 2 as described in Step 3 above.

If a Unit requires downloading a free trial of a software package, you should plan to complete the Unit and submit the assignment within the 30-day trial period.

Do the same for the remaining Units.

That's it. You are finished with Module 6B! Congratulations!!