Stat 321 – Probability and Statistics for Scientists and Engineers

 

Instructor:      Dr. Beth Chance

Class Times:   12:10-1:00, Monday Tuesday, Thursday: 10-111; Friday: 35-111B

Office:             Faculty Office Building East 25-103                        

Phone:            6-2961                                                 Email:             bchance@calpoly.edu            

Office Hours: M 11-12, T 1-2, R 1-3, F 11-12(35-111B), and by chance, appointment, and email

 

Course Webpages:    Blackboard (http://my.calpoly.edu)

http://statweb.calpoly.edu/bchance/stat321W08/

Course Listserv:        stat-321-01-2082@calpoly.edu

 

Overview

“We see that the theory of probability is at bottom only common sense reduced to calculation; it makes us appreciate with exactitude what reasonable minds feel by a sort of instinct, often without being able to account for it.  It is remarkable that this science, which originated in the consideration of games of chance, should have become the most important object of human knowledge.  The most important questions of life are, for the most part, really only problems of probability.” - Pierre Simon, Marquis de Laplace

 

“Statistics is like grout- the word feels decidedly unpleasant in the mouth, but it describes something essential for holding a mosaic in place.” – The Statistical Sleuth, by Fred L. Ramsey and Daniel W. Schafer

 

Probability is the mathematical study of uncertainty or randomness. Statistics, which may be defined as the science of gaining insight from data, is both an exciting intellectual discipline and a powerful scientific tool.  Although the famous mathematician Laplace no doubt overstated the point in the quote above, there is no denying that the concept of uncertainty pervades our everyday lives and that the mathematics of probability has become a very useful tool in a wide variety of fields.  Moreover, statistical thinking abounds in everyday life and statistical methods are used in most academic disciplines.  This course is an introduction to the fundamental concepts and methods of probability with an emphasis on their applications to statistics and data analysis.

 

Prerequisite: The prerequisite for this course is knowledge of differential and integral calculus for one variable, covered by Math 132 or Math 142 at Cal Poly. Specifically, we will use techniques of differentiation and integration, and infinite series. There will be no review of this material; you should consult your calculus text or meet with me if problems arise. We will also make occasional use of set theoretic properties and operations; these will be reviewed very quickly at the appropriate time. No prior knowledge of or familiarity with probability or statistics is assumed or expected.
Goals:  By the conclusion of the course, I hope that you have acquired:

 

Class Policies: Class time will be split roughly evenly between lectures and activities.  The activities are designed to lead you to discover concepts and to explore properties of probability and statistics.  While this process may take longer, it is my belief that it will better help you understand and retain the material.  Most of the activities will ask you to work with a partner, and many will ask you to use the computer.  We will discuss the activities after you complete them in an effort to ensure that you have individually garnered the intended lessons from them.  During lectures, you are sincerely encouraged to interrupt with questions and comments at any time. Class attendance is very strongly encouraged, for you are responsible for everything presented in class.

 

Required Texts/Materials:

·         Probability and Statistics for Engineering and the Sciences, 7th edition, Devore, J. L. (2008)

·         You should also have a USB drive, a scientific calculator, an email address, and a large three-ring binder.  You will need access to Minitab, Excel, and the internet outside of class. 

Additional lecture handouts will be supplied in class and lab, you are responsible for receiving and keeping these materials. Handouts from previous lectures will be available outside my office door and on the course web page. The handouts will consist primarily of activities that have been designed to help you learn the material, along with some exposition.  You will also be expected to read the text as a supplement and reference to what you learn in class. 

 

Computer Use: We will make fairly extensive use of computers in this course.  They will prove useful in at least three ways:

·         for performing calculations and creating graphics necessary for analyzing data

·         for conducting simulations to approximate long-run behavior of random phenomena

·         for addressing “what if” questions that allow you to explore concepts of probability and statistics

We will use both the statistical analysis package Minitab (version 15) and the spreadsheet Excel.  In addition to using Minitab to analyze data and perform simulations, you will write some small-scale programs with it as well.  No prior knowledge of these software tools is assumed; you will receive detailed instructions regarding their use when the need arises.  Minitab is freely available in the Library Learning Commons and you can also download a copy from the Technology panel of my.calpoly.edu (under Windows). (See green computer instructions handout.) You are also encouraged to bring a scientific calculator with you to each class session.

Grading Policies:  Your course grade will be based on the following components, with relative weight as indicated: You need to specify this choice by January 18.

            Option A                                                         Option B

            HWs                               15%                            

            Labs                               15%                             Labs                          15%

            Quizzes                           15%                             Quizzes                     20%

            Midterm Exams               35% (17.5% each)       Midterm Exams         40% (20% each)

            Final exam                       20%                             Final exam                25%

With Option B, you still have the option of turning in your homework and receiving feedback on your solutions.

 

Homework and Lab Assignments: The purpose of these homework and lab assignments is three-fold:

·         to give you the problem-solving practice necessary to learn, understand, and apply the concepts and techniques presented,

·         to provide you with feedback regarding your understanding of the material, and

·         to prepare you for the kinds of questions that will be on the exams.

Homework assignments will not be graded but you are highly encouraged to complete them as if they were and to see me in a timely fashion if you have questions on the homework problems.  Solutions to homework assignments will be posted on the course web page for your review.   There will be approximately 8 labs to be completed this quarter.  The lab assignments will tend to have more computer involvement than the homework questions. We will start the lab assignment during the Monday lab session but you are responsible for completing the lab writeup outside of class.  You are encouraged to work together with up to one other person on labs.  For each lab assignment, it is your responsibility to make sure both members do the work and learn the relevant material and computer skills.  Hand in one write up for the team, with both names, section number, etc. Labs should be typed, spell checked, and include all relevant computer output (ideally integrated into the body of the report).  Exemplary labs will be posted online after they are graded.

    

Quizzes and Exams: There will be approximately 6-8 quizzes during the quarter.  Tentative dates are listed in the schedule, but these may change without warning.  You should review solutions from previous homework, labs, and previous class’ material in preparation. If we take more than 5 quizzes, the lowest quiz grade will be dropped.  Some quizzes may be taken collaboratively with one or more partners when announced.  Quizzes may not be made up. 

     The purposes of these quizzes are:

·      to encourage and reward your attendance and engagement in class,

·      to motivate you to study the material on a continual basis,

·      to provide you with prompt feedback regarding your understanding of the material, and

·      to prepare you for the types of questions that will be on the exams.

 

     There will be two in class exams and one cumulative final.  Graded quizzes and exams will be returned in class or can be picked up from the instructor.  Exams can be made-up for students who notify me (with appropriate proof) at least two days before the exam of their unavoidable absence.

 

Study Hints: My expectation is that you will need to spend approximately 10 hours/week of your time on this four-unit class outside of the lecture time during the first eight weeks.  You should reserve at least one hour per week to look over your notes, review for quizzes, and formulate questions about the material, in addition to time reading the textbook and working on assignments.  It is important that you spend this time wisely and that you ask for help early when you are struggling. You are especially encouraged to start homework and lab assignments early in the week.  I and previous students in the class offer the following very simple pieces of advice for doing well in the course:

 

1. Come to class. Student evaluations reinforce my conviction that there is no substitute for attending class, seeing and hearing the material and examples presented, and having the chance to ask questions and to practice problems. I do present some material that is not covered in the text and cover some material in different ways than the text, as well. Finally, one can often pick up hints and advice about studying and about homework problems from attending class.

      

2. Participate in class. Coming to class only contributes to your learning if you are willing to participate actively. During many class periods you will be asked to work on activities designed to help you learn the material and to explore the concepts and methods of probability and statistics.  Please engage fully with these activities and do not disrupt the learning of others.

      

3. Work together. Many of the in-class activities will ask you to work collaboratively with your peers.  Please do so freely, as I believe that you will be able to help each other with your learning.  I also encourage you to work and study together outside of class.  Just remember that unless specified otherwise, solutions to all problems are to be written up individually.

      

4. Ask questions. Please do not hesitate to ask me questions when you don’t understand something presented in class or on a homework problem. Don’t necessarily wait until after class or during office hours; you can ask questions during class time as well. Feel free to give me other sorts of feedback as well: whether the pace is too fast or slow, etc.

      

5. Review your notes. My intention is to enable you to put together a very extensive and useful set of class notes. I urge you to keep thorough notes and to review them often, particularly before starting homework assignments and while studying for exams.

      

6. Start the assignments early.  You will be given at least one week to complete each assignment. Please avoid the temptation to put the assignments off until the last day; you should start early enough to be able to ask questions when they arise. It is also helpful to have the homework problems in mind when we cover the relevant material in class.

      

7. Take the course seriously.  This course is designed to take roughly 10 hours/week outside of class time.  One aspect of the course is that it abounds with “word problems;” you will be expected to set up problems mathematically as well as to solve them. You will also need to remember and apply many concepts and techniques of calculus. Another facet is that you will be responsible for doing some small-scale derivations and proofs.

      

8. Have fun with the material.  This may seem to contradict the previous point, but I do think that probability and statistics are very fun, entertaining subjects. We will be analyzing genuine data from a variety of real-world applications, and we will be discussing games and puzzles, as well. Allow yourself to enjoy these aspects of the course, and feel free to suggest other applications that appeal to you.

      

9. Think! Do not treat the course as an exercise in mere “plug-and-chug” number-crunching, and do not try to apply formulas by rote to solve problems. (That’s not what statistics is about!) Think about what you are doing, recognizing that there are often several ways to solve a problem and that one clever thought might eliminate the need for pages of painful calculations. Use your intuitive sense about probability and uncertainty to check your results.

           

Above all, you are responsible for your own learning.  As your instructor, my role is providing you with contexts and opportunities to facilitate the learning process.  Please call on me to help you with this learning in whatever ways I can.

 

Daily Responsibilities:

It is my expectation that you will spend time on this course over several different days during the week.  This will help both with your time management and your retention and integration of the material.  In general, in addition to staying up on your reading in the textbook, you will have the following responsibilities:

            Weekend: Review the most recent material, work on lab and homework assignments.

Mondays:  Ask questions (about the reading, homework assignment, lab assignment) in class.

Tuesdays: Turn in the homework assignment.

Wednesdays: Review homework solutions, prep for quiz, work on lab.

Thursdays: Take quiz in class, ask remaining lab questions.

Fridays: Submit lab, begin next lab assignment.

 


Stat 321 – Tentative Schedule 

 

 

Date

Read

Material

Assignment Due

Collecting and Examining Data

 

1

M

1/7

1.1

Overview, Minitab (Lab 1 - FCI)

 

2

T

1/8

1.2, 1.3

Descriptive Statistics

Online survey

 

3

R

1/10

1.4

Descriptive Statistics (cont.)

 

 

Probability

 

 

F

1/11

 

Lab 2 – Random Babies

Lab 1

 

4

M

1/14

2.1

Probability

 

 

5

T

1/15

2.2

Rules for Calculating Probabilities

HW 1

 

6

R

1/17

2.3

Counting Techniques

Quiz 1

 

 

F

1/18

 

Lab 3 – The Birthday Problem

Lab 2

 

 

M

1/21

 

No classes

 

 

7

T

1/22

2.4, 2.5

Conditional Probability, Independence

HW 2

 

8

R

1/24

2.4

Law of Total Probability

Quiz 2

 

9

F

1/25

2.4

Bayes’ Theorem, Misconceptions

Lab 3

 

 

M

1/28

 

Review

 

 

 

T

1/29

 

Exam 1 – Ch. 1 and 2

 

 

Random Variables

 

10

R

1/31

3.1-3.2

Discrete Random Variables

 

 

 

F

2/1

3.3

Lab 4 – Comparing Roulette Bets

 

 

11

M

2/4

3.4

Binomial Probability Distribution

 

 

12

T

2/5

3.5, 3.6

Other Discrete Distributions

HW 3

 

13

R

2/7

4.1-4.2

Continuous Random Variables

Quiz 3

 

 

F

2/8

 

Lab 5 – Modelling Earthquake Magnitudes

Lab 4

 

14

M

2/11

4.3

Normal Distribution

 

 

15

T

2/12

4.4, 4.5

Other Continuous Distributions

HW 4

 

16

R

2/14

 

Examples

Quiz 4

 

 

F

2/15

 

No classes

 

 

 

M

2/18

 

Review

Lab  5

 

 

T

2/19

 

Exam 2 – Ch. 3 and 4

 

 

Several Random Variables

 

17

R

2/21

5.1-5.3

Combining Random Variables

 

 

 

F

2/22

 

Lab 6 – Sampling Distributions

 

 

18

M

2/25

5.4

Central Limit Theorem

 

 

19

T

2/26

5.5

Central Limit Theorem Calculations

HW 5

 

Estimation

20

R

2/28

7.1

Confidence Intervals

Quiz 5

 

F

2/29

 

Lab 7 – What is meant by confidence

Lab 6

21

M

3/3

7.2

Confidence Intervals (cont.)

 

22

T

3/4

7.3

One Sample t intervals

HW 6

23

R

3/6

6.1

Point Estimation

Quiz 6

 

F

3/7

 

Lab 8 – German Tanks

Lab 7

24

M

3/10

6.2

Methods of Point Estimation

 

25

T

3/11

 

Methods of Point Estimation (cont.)

HW 7

26

R

3/13

 

Bootstrapping

Quiz 7

 

F

3/14

 

Review Me

Lab 8

 

M

3/17

 

Final: 10:10-1:00

 

 

Important Dates:        Jan. 16 – last day to drop/add classes