Statistics

Fall 2007

Introduction 2Wed, Aug 22, 2007

Introduction

Dr. Robb T. Koether Office: Bagby 114 Office phone: 223-6207 Home phone: 392-8604 (before 11:00 p.m.) Office hours: 2:30-4:00 MWRF, 3:30 – 4:00 T

Other hours by appointment E-mail: rkoether@hsc.edu Web page:

http://people.hsc.edu/faculty-staff/robbk

Introduction 3Wed, Aug 22, 2007

The Course

The class meets in Bagby 022 at 8:30 - 9:20 MWF and at 2:30 – 3:20 T.

The text for the course is Interactive Statistics, 3rd ed., by Martha Aliaga and Brenda Gunderson.

The web page for this course is at

http://people2.hsc.edu/faculty-staff/robbk/Math121

Introduction 4Wed, Aug 22, 2007

Introduction

Syllabus Lectures Assignments Page xi – Interactive Exercises Page xvi – Graphing Calculator

Introduction 5Wed, Aug 22, 2007

Grading

There will be Weekly quizzesThree testsA final exam

Introduction 6Wed, Aug 22, 2007

Grading

In the final average, these will have the following weights:

Category Weight

Average of quizzes 30%

Average of the tests 50%

The final exam 20%

Introduction 7Wed, Aug 22, 2007

Homework

The homework is the most important part of this course.

Learning mathematics requires gaining knowledge and understanding, but more importantly doing mathematics is a skill.

You should not expect to acquire a skill by listening to a lecturer talk about it. It takes practice.

Do all of the homework every day.

Introduction 8Wed, Aug 22, 2007

Homework

More importantly, do not put off doing the homework until the night before the quiz.

You will not be able to learn that much material in one night.

Most importantly of all, do not put off doing the homework until the day before a test.

By then it is too late to learn it.

Introduction 9Wed, Aug 22, 2007

Homework

At the beginning of each class meeting (except on Tuesdays), I will spend up to 10 minutes working one or two homework problems in detail from previous assignments.

You may request a problem that you would like to see worked.

Of course, outside of class, I will help you with as many problems as I can.

Introduction 10Wed, Aug 22, 2007

Quizzes

Each Tuesday there will be a 10-minute quiz.

The quiz will contain 1 to 3 questions taken from the previous week's homework assignments.

The problems will be copied verbatim from the book.

Introduction 11Wed, Aug 22, 2007

Tests

The test schedule is as follows:

Test Date Coverage

#1 Fri, Sep 21 Chapters 1, 2, 3, 4

#2 Fri, Oct 19 Chapters 5, 6, 7

#3 Fri, Nov 16 Chapters 8, 9, 10, 11

Introduction 12Wed, Aug 22, 2007

The Final Exam

The final exam will be cumulative. It will be given in this classroom at the time

stated in the exam schedule. Everyone must take it. It will not be rescheduled. Do not schedule a flight home before the

exam! You will lose your ticket.

Introduction 13Wed, Aug 22, 2007

Attendance

Attendance will be checked at the beginning of each class.

Two late arrivals will be counted as one absence.

The only valid excuses for missing class are An illness which includes a visit to the Health Center

or a doctor An approved college activity A true emergency Any absence excused by the Dean of Students

Introduction 14Wed, Aug 22, 2007

Attendance

Sending me an e-mail or leaving me a voice message does not excuse you from class.

Introduction 15Wed, Aug 22, 2007

Attendance

When assigning final grades, attendance will be taken into account.

Absences Action

0 – 2 Grade bonus

3 – 5 Neutral

6 – 8 Grade penalty

> 8 Withdrawal

Introduction 16Wed, Aug 22, 2007

Calculators

A calculator will be necessary for this course.

I strongly recommend the TI-83 or the TI-84.

Introduction 17Wed, Aug 22, 2007

The Honor Code

Quizzes, tests, and the final exam are pledged.

Introduction 18Wed, Aug 22, 2007

Classroom Etiquette

During a lecture, you are free to ask questions. It is polite to raise your hand first and wait to be

called on. You should not talk to other students while I am

talking. While working assigned problems in class, you

are free to talk to other students provided you are talking about the assigned problems.

Introduction 19Wed, Aug 22, 2007

Classroom Etiquette

Do not make leave the room during the class. If necessary, use the bathroom before coming to

class. If you are thirsty, get a drink before class.

Do not sleep in class. Do not work on assignments from other classes

during class. Do not read the newspaper during class.

Introduction 20Wed, Aug 22, 2007

Goals of this Course

To learn statistics.The theoretical basis of the statistical method.How to perform statistical tests.How to interpret statistics.

To become a more sophisticated thinker. To become a more sophisticated

consumer of information.

Introduction 21Wed, Aug 22, 2007

Goals of this Course

To get you through your freshman year with a decent GPA.

Introduction 22Wed, Aug 22, 2007

The Scientific Method

Formulate a theory. Collect some data. Summarize the results. Make a decision.

Introduction 23Wed, Aug 22, 2007

The Scientific Method

Formulate a theory – Chapter 1. Collect some data. Summarize the results. Make a decision.

Introduction 24Wed, Aug 22, 2007

The Scientific Method

Formulate a theory – Chapter 1. Collect some data – Chapters 2 – 3. Summarize the results. Make a decision.

Introduction 25Wed, Aug 22, 2007

The Scientific Method

Formulate a theory – Chapter 1. Collect some data – Chapters 2 – 3. Summarize the results – Chapters 4 – 5. Make a decision.

Introduction 26Wed, Aug 22, 2007

The Scientific Method

Formulate a theory – Chapter 1. Collect some data – Chapters 2 – 3. Summarize the results – Chapters 4 – 5. Make a decision – Chapters 9 – 14.

Introduction 27Wed, Aug 22, 2007

The Scientific Method

Formulate a theory – Chapter 1. Collect some data – Chapters 2 – 3. Summarize the results – Chapters 4 – 5. Make a decision – Chapters 9 – 14. Theoretical underpinnings – Chapters 6 –

8.

Introduction 28Wed, Aug 22, 2007

Formulate a Theory

We are wondering whether a particular die is fair.

That is, does each number occur just as often as every other number?

For example, if we roll the die 600 times, we expect to get each number 100 times.

Introduction 29Wed, Aug 22, 2007

Formulate a Theory

Or do we?

Introduction 30Wed, Aug 22, 2007

Formulate a Theory

The theory that the die is fair will be tested by posing it as a question with two competing answers.

Question: Does the distribution of observed rolls match what we would expect to see if the die were fair?

Introduction 31Wed, Aug 22, 2007

Formulate a Theory

The possible answers (yes and no) are stated more precisely as two competing hypotheses:“Null hypothesis” The die is fair.

Any deviations from the expected observation are due entirely to chance.

“Research hypothesis” The die is not fair. Any deviations from the expected observations are

due to the bias in the die.

Introduction 32Wed, Aug 22, 2007

Collect Some Data

So we roll the die 600 times and get the following results.

Number 1 2 3 4 5 6

Expected 100 100 100 100 100 100

Observed 95 106 89 97 97 116

Introduction 33Wed, Aug 22, 2007

Two Possible Explanations

There is a discrepancy. Can it be explained by chance?

Introduction 34Wed, Aug 22, 2007

Summarize the Results

We use the TI-83 or TI-84, and compute a special quantity:

2 = 4.56.

Introduction 35Wed, Aug 22, 2007

Summarize the Results

We use the TI-83 or TI-84, and compute a special quantity:

2 = 4.56. So what?

Introduction 36Wed, Aug 22, 2007

Summarize the Results

If the die really is fair, then statistical theory says that we expect this calculation to yield a value between 0 and 11.070, with the value expected to be very close to 5.

Introduction 37Wed, Aug 22, 2007

Make a Decision

Since 2 is within this range, we conclude that the “null hypothesis” is correct:

The die is fair.

Introduction 38Wed, Aug 22, 2007

An Important Question

Does this procedure prove that the die is fair?

Introduction 39Wed, Aug 22, 2007

An Objection

Our antagonist was arguing that this die turned up 6’s too often.

He claims that our data supports his assertion.

How do we deal with that?

Introduction 40Wed, Aug 22, 2007

Collect More Data

So we roll the die 6000 times and get the following results.

Number 1 2 3 4 5 6

Expected 1000 1000 1000 1000 1000 1000

Observed 945 983 1023 1015 1000 1034

Introduction 41Wed, Aug 22, 2007

Collect More Data

This time we get 2 = 5.224. This is extremely close to the value that

the theory predicts for a fair die. At this point, we tell our antagonist to go

study statistics.