Math 5 - CHANCE, Fall 1996


      John Finn                             Shunhui Zhu
1S Bradley 316 Bradley


Course Description

Class 1 Lotto

Class 2 Teenagers and smoking

Class 3 PSAT bias and JMP

Class 4 Average and Standard Deviaton

Class 5 Standard Deviaton; Stephen Jay Gould on batting .400

Class 6 Introduction to Probability

Class 7 The Binomial Distribution

Class 8 Margin of Error

Class 9 Polling, Standard Error, Normal Distribution

Class 10 Standard Error, Normal Approximation; Projects

Class 11 Surveys and Data Collection

Class 12 Correlation and Regression

Class 13 Correlation & Regression, and Immigration Statistics

Class 14 Correlation & Regression; Conditional Probability

Class 15 Economics, Streaks and Tversky

Course Description

Welcome to Chance!

Chance is an unconventional math course. The standard elementary math course develops a body of mathematics in a systematic way and gives some highly simplified real-world examples in the hope of suggesting the importance of the subject. In Chance , we will choose serious applications of probability and statistics and make these the focus of the course, developing concepts in probability and statistics only to the extent necessary to understand the applications. The goal is to make you better able to come to your own conclusions about news stories involving chance issues.

Topics that might be covered in Chance include:

During the course, we will choose a variety of topics to discuss, with special emphasis on topics currently in the news. We will start by reading a newspaper account of the topic in a newspaper likeTh e New York Times or The Boston Globe. We will read other accounts of the subject as appropriate, including articles in journals like Chance magazine, Science, Nature, and Scientific American, and also original journal articles. We will supplement these articles by readings on the basic probability and statistics concepts relating to the topic. We will use computer simulations and statistical packages to better illustrate the relevant theoretical concepts.


The class will differ from traditional math classes in organization as well as in content: The class meetings will emphasize group discussions, rather than the more traditional lecture format. Students will keep journals to record their thoughts and questions. Additional homework will be assigned regularly. There will be a major final project in place of a final exam.

Scheduled meetings

The class meets Tuesday and Thursday from 10:00 to 11:50 a.m. in Filene Auditorium, on the first floor of Bradley/Gerry Halls.

Discussion groups

Discussions are central to the course and usually focus on a current article in the news. They provide a context in which to explore questions in more depth and understand material better by explaining it to others.

Every member of each group is expected to take part in these discussions and to make sure that everyone is involved: that everyone is being heard, everyone is listening, that the discussion is not dominated by one person, that everyone understands what is going on, and that the group sticks to the subject.


The text for the course is Statistics, second edition by Freedman, Pisani, Purves and Adhikari (FPPA), available from the Dartmouth Bookstore and Wheelock Books. Students will also learn to use the JMP statistical package that is available from the public server as a key served application.


Each participant should keep a journal for the course. This journal will include:

A good journal should answer questions asked, and raise questions of your own, with evidence that some time has been spent thinking about the questions. In addition, there should be evidence of original thought: evidence that you have spent some time thinking about things that you weren't specifically asked about. In writing in your journal, exposition is important. If you are presenting the answer to a question, explain what the question is. If you are giving an argument, explain what the point is before you launch into it. What you should aim for is something that could communicate to a friend or a colleague a coherent idea of what you have been thinking and doing in the course.

We encourage you to cooperate with each other in working on anything in the course, but what you put in your journal should be your own alone. If it is something that has emerged from work with other people, write down who you have worked with. Ideas that come from other people should be given proper attribution. If you have referred to sources other than the texts for the course, cite them.

Journals will be collected and read on these dates:

Thursday   10   October 
Thursday 24 October
Thursday 7 November
Thursday 21 November
Tuesday 3 December


To supplement the discussion in class and assignments to be written about in your journals, we will assign readings from your text FPPA, together with accompanying homework. When you write the solutions to these homework problems, you should keep them separate from your journals. Homework assignments will be assigned once a week and should be handed in on Thursdays.

Final project

We will not have a final exam for the course, but in its place, you will undertake a major project. This project may be a paper investigating more deeply some topic we touch on lightly in class. Alternatively, you could design and carry out your own study. Or you might choose to do a computer-based project. To give you some ideas, a list of possible projects will be circulated. You can also look at some previous projects on the Chance Database. However, you are also encouraged to come up with your own ideas for projects.

Chance Fair

At the end of the course we will hold a Chance Fair, where you will have a chance to present your project to the class as a whole, and to demonstrate your mastery of applied probability by playing various games of chance. The Fair will be held during the final examination time assigned by the registrar.


Materials related to the course will be kept on our web site and on Kiewit PUBLIC server (PUBLIC: Courses & Support: Academic Departments & Courses: Math: Chance). In addition supplementary readings will be kept on reserve in Baker Library.

Class 1 Lotto

September26, 1996
Class Discussion

How to play NH Powerball


1. Journal assignment: Find two articles in recent newspapers that are appropriate for the course. In your journals, describe what each is about in three or four sentences. Come up with some questions like those in Chance News. (Due Tuesday)

2. Read Chapters 1 and 2 from FPPA. Do the review exercise at the end of Chapter 2 on page22. (Due Thursday)

Class 2 Teenagers and smoking

1 October ,1996
Group discussion:

Read the article "Study Finds Stunted Lungs in Young Smokers".

On Table 1 from "Effects of Cigarette Smoking on Lung Function in Adolescent Boys and Girls" in The New England Journal of Medicine, 26 Spetember 1996.

Study the table.

What conclusions would you draw from the table?

Is there any relation between maternal smoking and child smoking?

Do you think there are significant differences between boys and girls with respect to smoking?

What confounding factors might explain these differences between boys and girls?

Coming attractions.

David A. Kessler, M.D., the controversial commisioner of the Food and Drug Aflmin- istration (FDA) will give a lecture Thursday 10 October at 7:30 p.m. in Cook Auditorium in Murdough Center. Kessler will examine health issues and FDA's evolving policy concerning tobacco.

Class 3 PSAT bias and JMP

October 3, 1996

Class Discussion

1. Read the article handed out in class: "College Board Revises Test to Improve Chances for Girls"

2. Discuss the following questions:
a. What kinds of bias are discussed in the article?
b. Are they measurement biases?

Look at both Math5 Survey and data, MALS Survey and data.


Chapter 3 , all review exercises.
Chapter 4 , Review Problems: 1-3, 5, 7-10, 13, 14.
Read Chapter 6.

Class 4 Average and Standard Deviaton

8 October ,1996

Class discussion: PSAT modifications.

Read "College Board Revises Test to Improve Chances for Girls", by Karen W. Arenson; The New York Times. Wednesday 2 October 1996

Discussion questions:

Introducing Average and Standard Deviation

More on using JMP

Journal assignment

Class 5 Standard Deviaton; Stephen Jay Gould on batting .400

October 10, 1996

Class discussion: Do Prisons Reduce Crime?

Read "Incarceration Is a Bargain", by Steve Hanke, in The Wall Street Journal, Monday, 23 September 1996.

Discussion questions:

Standard Deviation

Discussion of Stephen Jay Goild's 'Why the Death of 0.400 Hitting Records Improvement of Plays' (from his Full House, Harmony Books, 1996).

Journal assignment

Don't forget your two article summaries, which are due Tuesday. When you summarize an article, be sure to include the publication it comes from and the date.

Homework: Read chapters 13 and 14 ("What Are the Chances" and "More about Chance" in FPPA. Do the even Review Exercises in chapter 13, and odd Review Exercises in chapter 14.

Class 6 Introduction to Probability

October 15, 1996

Class Discussionthe celerated Birthday Problem.

Discussion questions (break into groups of 4):
The Mathematics of the Birthday Problem

Video clip: What is Probability? (from the Against All Odds video series on probability and statistics)

Coincidences in Airplane Crashes

Coin Classing Experiment

Journal assignment Think of coincidences in your own life. What is the likelihood of these being random chance occurrences? Are they really events that have occurred against all odds?

Class 7: The Binomial Distribution

October 17, 1996

Small Group Activity: Coke vs. Pepsi.

a. Break into groups of four.

b. Identify a member of your group who claims to be able to tell the difference between Pepsi and Coke. (Coke Classic, that is; accept no substitutes!)

c. Design an experiment to test whether this is true. Remember that one swallow doth not a summer make: Don't certify your taste-tester just on the basis of one taste. Write down exactly what data you will collect and what you will do with the data before you start collecting it.

d. What is being tested?
e. Carry out the experiment.
f. Record your results.

The Binomial Distribution

Journal assignment

Don't forget your two article summaries, which are due Tuesday. When you summarize an article, be sure to include the publication it comes from and the date.

Homework assignment. In FPPA:

Class 8 Margin of Error

October 22, 1996

Margin of Error

1. The CNN Tracking Poll for October 19-20 interviewed 732 likely voters. They reported that 55% favored Clinton, 34% favored Dole and 6% favored Perot with a sampling error of + or - 4% (sampling error is also called margin of error).

2. The New York Times often puts at the end of an article about a poll, an explanation of how their poll was carried out. In a recent poll of 1,166 people, the article stated that the margin of error was 3%. In their explanation of how the poll was carried out they explained the margin of error by the statement "In theory, in 19 cases out of 20 the results based on such samples will differ by no more than three percentage points in either direction from what would have been obtained by seeking out all American adults." 3. Read the NYT article "Use of Daily Election Polls Generates Debate in Press" (Oct. 4, 1996). Consider the following questions:
Journal Questions

(1) Read the NYT article "Misreading the Gender Gap" by Carol Tavris (September 17,1996), What do you think of her explanation of the gender gap in the current election.

(2) How would you explain "margin of error" to a friend who had not had a statistics course?

Class 9: Polling, Standard Error, Normal Distribution

October 24, 1996

Speaker: Tami Buhr from Harvard University will speak on her experiences in polling.

Standard Error, Normal Distribution.

Homework Assignment: Read Chapters 19, 20, 21.

(We will be discussing a couple of the ideas from Chapter 18 in class. If you miss the class or need additional support, you may want to look through that chapter.)

Preliminary Project Proposal:

Please hand in a separate sheet with a brief description of your project proposal next Thursday. We will talk more about this is class Wednesday.

Journal assignment

Comments and reflections on speaker's talk.

Class 10 Standard Error, Normal Approximation; Projects

October 29, 1996

Standard Error and Normal Approximation
by John Finn

And some review of the mathematics that has come up so far. We're going to try to make firm the mathematics behind chance quantities, particularly sums of draws from a box.

About Your Chance Project

Remember that you're to hand in Thursday a a brief description of your project proposal. We'll talk about ideas for projects and our policies on them.

Class 11 Surveys and Data Collection

October 31, 1996

Guest Speaker: Nancy Mathiowetz of the University of Maryland will speak on Surveys and Data Collection.

Confidence Intervals and Standard Deviation

Homework assignment:

(If you need a review of how to plot lines, find slopes, etc., read Chapter 7)

Journal assignment

Don't forget your two article summaries, which are due Tuesday. When you summarize an article, be sure to include the publication it comes from and the date.

Class 12 Correlation and Regression

Tuesday 5 November, 1996

SE, Normal Approximation and Margin of Error

We read about a poll taken to estimate what percentage of the population are voting for each of several candidates. The results say that "57% are for Millard Fillmore, with a 3% margin of error". What does this mean, and how do the pollsters come up with it?

Class discussion: You be the judge: did regression analysis reveal a voting fraud, and was the fraud decisive?

Read "Probabilty Experts May Decide Pennsylvania Vote" ( The Nets York Times, 11 April 1994).

Discussion questions:

Scatter Diagrams, and Correlation and Regression

Quantifying the degree of association between two variables:

Class 13 Correlation & Regression, and Immigration Statistics

Thursday 7 November 1996

Guest Speaker: Prof. Richard Wright: The Satistics of Immigration Prof. Wright is the Chair of Dartmouth's geography department.

Human Subjects

1. Elizabeth Bankert, Assistant Director of Grants & Contracts here at Dartmouth, will talk about guidelines for carrying out projects that involve human subjects (which include any sort of survey), and Dartmouth's regulations on these matters.

Correlation and Regression.

What are the SD line and the regression line of a scatter diagram? How do we determine them, and what do they tell us about the data?

Homework Assignment

Class 14 Correlation & Regression; Conditional Probability

Tuesday 12 November 1996

Correlation and Regression.
What are the SD line and the regression line of a scatter diagram? How do we determine them, and what do they tell us about the data?

Class discussion: Conditional probability and false positives.

1. In one of Marilyn vos Savant's columns in Parade magazine a reader asked

Suppose we assume that 5So of the people are drug-users. A test is 95So accurate, which we'll say means that if a person is a user, the result is positive 95So of the time; and if she or he isn't, it's negative 95Wo of the time. A randomly chosen person tests positive. Is the individual highly likely to be a drug-user?

Marilyn's answer was:

Given your conditions, once the person has tested positive, you may as well flip a coin to determine whether she or he is a drug-user. The chances are only 50-50.

How can Marilyn's answer be correct?

2. An article in The New York Times some time ago reported that college students are beginning to routinely ask to be tested for the AIDS virus.

The standard test for the HIV virus is the Elisa test that tests for the presence of HIV antibodies. It is estimated that this test has a 99.8% sensitivity and a 99.8% specificity. 99.8Wo specificity means that, in a large scale screening test, for every 1000 people tested who do not have the virus we can expect 998 people to have a negative test and 2 to have a false positive test. 99.8So sensitivity means that for every 1000 people tested who have the virus we can expect 998 to test positive and 2 to have a false negative test.

The Times article remarks that it is estimated that about 2 in every 1000 college students have the HIV virus. Assume that a large group of randomly chosen college students, say 100,000, are tested by the Elisa test. If a student tests positive, what is the chance this student has the HIV virus? What would this probability be for a population at high risk where 5Wo of the population have the HIV virus?

If a person tests positive on an Elisa test, then another Elisa test is carried out. If it is positive then one more confirmatory test, called the Western blot test, is carried out. If this is positive the person is assumed to have the HIV virus. In calculating the probability that a person who tests positive on the set of three tests has the disease, is it reasonable to assume that these three tests are independent chance experiments?

Journal assignment

Read and comment on the Manchester, NH Union Leader story "Exit Poll Wrong Call in Senate Race Leaves Anger, Hurt, Red Faces". There are a couple of discussion questions at the end of the article.

Class 15 Economics, Streaks and Tversky

Thursday 14 November 1996

Guest speaker: Professor Michael Knetter of Dartmouth's Economics Department will speak on the role of statistics in economics.

Activity: recognizing streaks
We will demonstrate a computer simulation of three coins: