# Mathematics

## Math 130: Introductory Statistics

Spring 2000: 3 credits, MRF, 1:10-2:00, NC204
Instructor: Rich Maresh, Associate Professor
Office: MC 522, 796-3655, Hours: M 12-1, R 9-10, R 2-3, F 12-1 (Home: 526-4988)
Final Exam: Wednesday, 10 May 00, 7:40-9:40

Course Description: An introductory course which deals with the organization and processing of various types of data, normal and binomial distributions, estimation theory, hypothesis testing, correlation and regression, analysis of variance, and, time permitting, some non-parametric tests. NOT open to students who have earned credits or are concurrently enrolled in MATH 230. Prerequisite: acceptable placement exam or grade of C or higher in MATH 001. Recommended for general education requirements, B.S. degree.

Text: Elementary Statistics, 7th Editioin (Triola, Addison-Wesley Publishing, 1997)

CORE SKILL OBJECTIVES
1. Thinking Skills:
A. Uses reasoned standards in solving problems and presenting arguments.
2. Communication Skills:
A. Reads with comprehension and the ability to analyze and evaluate.
B. Listens with an open mind and responds with respect.
3. Life Values:
A. Analyzes, evaluates and responds to ethical issues from an informed personal value system.

COURSE OBJECTIVES
1. Thinking Skills:
A. Reasons. deductively by learning general principles which are then applied to specific problems.
B. Reasons inductively by studying examples, seeing the common characteristics, and broadening the solution to the generic case.
C. Learns to use the statistical process as one of the means of answering a question or supporting a position.
2. Communication Skills:
A. Reads text and reference materials outside of class.
B. Observes examples and discusses questions in class.
C. Communicates solutions to statistical problems in writing on quizzes and exams in appropriate statistical format.
3. Life Value Skills:
A. Learns of some classic examples of the misuse of statistics and its consequences.
B. Acquires an appreciation for the importance of honesty in the presentation of all (not just favorable) outcomes of statistical research.
4. Specific Objectives in a Statistics Course:
A. Learn to use the tools of descriptive statistics.
B. Understand the difference between a population and a sample.
C. Understand the Central Limit Theorem and its implications for inferential. statistics.
D. Be able to use the appropriate statistical test to draw conclusions about a population.

COURSE PROCEDURES:

Statistics is one of the most useful branches of the mathematical sciences – it is the tool of choice for research in most of the medical and social sciences. It is the language in which results in those disciplines are couched. More than in most courses, the material in this course hangs together – there is one "big idea" upon which it all hinges: the Central Limit Theorem is the concept which allows us to draw all sorts of conclusions about an entire population from a random sample of data collected from that population.

Reading the Text: The text book presents the material from a conceptual perspective, but also offers many worked examples which can be used to model the appropriate procedures for the problems we encounter. There is also a regular commentary regarding the use of technology. Please READ the BOOK!

Calculator: All the computations we will do in the course can be done "by hand" (i.e., by means of a \$10-\$15 calculator…), but I will be making regular use of a TI-83 calculator as an overhead display device. I strongly urge you to consider purchasing a TI-83 for yourself. It is designed for an introductory statistics course such as this one, and virtually everything we do in the course can be done at the push of a few buttons. The text makes frequent references to this particular calculator, as will I in class. The current cost is about \$100, so even though they are not "cheap", they cost about as much as a nice pair of walking shoes. Your life will be much easier if you can focus on the concepts rather than on the computation. Think about it.

Homework: There will be daily assignments. They will not generally be collected but these problems form the CORE of the learning process throughout the course. There is a traditional standard that a college student should expect to spend about 2 hours outside of class for each 1 hour in class; I think this is about right. You may find that once in a while you cannot manage to do all the assigned problems, and I don’t have a problem with that – but you do need to make sure you are putting in the time necessary to learn the material. I will generally begin class by asking for questions on the homework – it is extremely important that you ask questions when you have them, and that you do enough work so that you know when you do have questions.

Exams: I do not expect you to memorize all the various formulas we will encounter during the course. Your job is to learn which formula is appropriate for which problems and to use them accurately and correctly. You are allowed a sheet of notes for each chapter, basically an outline – and these may be brought in to the exams. You may also use the entire collection of these chapter outlines for each exam.

Grading Procedures: There will be 3 exams during the course, as indicated on the schedule, and a cumulative final exam. The final will have a stronger emphasis on the material in the last few chapters, since we won’t have a separate exam on those topics, but it will include material from throughout the course. In fact, the key thing you need to learn is how to analyze a problem and decide what is the appropriate statistical method to use, and a cumulative exam is the only way I can see if you have been successful.
The first 3 exams will be 100 points each and the final will be worth 150 points. There will also be an occasional problem set collected along the way and the final project is worth 50 points. I anticipate having something like 700 points possible during the semester. I use the fairly "standard" scale: 90% for an "A", 80% for a "B", 70% for a "C", and 60% for a "D".

Final Project: This course lends itself to doing a "project", and so I will give you the opportunity to use the statistical tools we have developed to investigate a real world question. The text offers a list of suggestions on pages 704-707. You may choose to do one of those, or you may want to develop a project of your own. You may want to investigate whether nursing majors drink more coffee than non-nursing majors. Or how much time students in statistics classes actually spend studying statistics each week, on average. Perhaps whether female college students are more likely than male college students to smoke. Please give this topic some thought over the first 8 or 10 weeks of the course. I will ask you to turn in your proposal on Monday, April 3. This should be a one-page write-up explaining what you are investigating and how you plan to collect your data and process it; I want to make sure you are barking up the right tree. Then the project will come due on the last day of class, Friday, May 5. The project will be worth 50 points, so it is worth your doing! You may work on this final project either alone or in pairs – let me know which at the time you turn in your proposal.

Americans with Disabilities Act: If you are a person with a disability and require any auxiliary aids, services, or other accommodations for this class, please see me and/or Wayne Wojciechowski, the campus ADA coordinator (MC 320, 796-3085), within ten days to discuss your needs.

MATH 130 Spring 2000 Schedule

17 Jan          1.2, 1.3   Overview, The Nature of Data                        p 9 # 1-17 odd; p 14 # 1-15 odd
20 Jan          1.4, 1.5   Design of Experiments                                     p 23 # 1-15 odd; p 27 # 1-8
21 Jan          2.2, 2.3   Graphing Data                                                   p 43 # 1-15 odd, 21, 23; p 55 # 1-15 odd

24 Jan         2.4   Measures of Central Tendency                             p 70 # 1-17 odd
27 Jan         2.5   Measures of Variation                                            p 87, # 1, 3, 5, 7, 13, 15, 17, 21
28 Jan         2.6   Measures of Position                                              p 99 # 1-19 odd

31 Jan         3.2, 3.3, 3.4   Basics of Probability                                p 130 # 7-14, 19, 23 p 140 # 5-13 odd; p 151 # 5-13 odd
3 Feb           3.5, 3.6   Combinatorics                                                  p 158 # 1, 3, 5; p 168 # 1-27 odd
4 Feb           4.2, 4.3   Random Variables, Binomial Experiments    p 193 # 1-17 odd; p 206 # 1-23 odd

7 Feb           4.4   The Binomial Distribution                                      p 213 # 1-15 odd
10 Feb             Review …
11 Feb                 EXAM #1

14 Feb         5.2   The Standard Normal Distribution                       p 240 # 1-33 odd
17 Feb         5.3, 5.4   Normal Distributions                                       p 246 # 1-13 odd; p 252 # 1-13 odd
18 Feb         5.5   The Central Limit Theorem                                    p 262 # 1-17 odd

21 Feb        5.6   Normal Approximation to Binomial Distrib.         p 273 # 1-23 odd
24 Feb        6.2   Estimating Pop. Mean: Large Samples                 p 301 # 1-19 odd
25 Feb        6.3   Estimating Pop. Mean: Small Samples                  p 313 # 1-17 odd

28 Feb        6.4   Estimating Population Proportion                         p 321 # 1-23 odd
2 Mar          6.5   Estimating Population Variance                            p 333 # 1-13 odd
3 Mar             EXAM #2

13 Mar        7.2 Fundamentals of Hypothesis Testing                    p 357 # 1-11 odd
16 Mar        7.3 Testing Claim about a Mean: Large Samples        p 372 # 1-15 odd
17 Mar        7.4 Testing Claim about a Mean: Small Samples         p 383 # 1-17 odd

20 Mar        7.5   Testing a Claim about a Proportion                       p 392 # 1-17 odd
23 Mar        7.6   Testing a Claim about a Standard Dev                  p 400 # 1-7 odd
24 Mar        8.2   Infer about Two Means: Depend Samples           p 421 # 1-13 odd

27 Mar       8.3   Infer about 2 Means: Indep, Large Samples         p 432 # 1-13 odd
30 Mar       8.4   Comparing Two Variances                                       p 440 # 1-9 odd
31 Mar       8.5   Infer about 2 Means: Indep, Small Samples          p 454 # 1-9 odd

3 Apr         8.6   Inferences about Two Proportions                          p 465 # 1-11 odd
6 Apr             Review …
7 Apr                 EXAM #3

10 Apr        9.2   Correlation                                                                  p 490 # 1-11 odd
13 Apr        9.3   Regression                                                                  p 505 # 1-11 odd
14 Apr        9.4   Variation, Prediction Intervals                                 p 515 # 1-11 odd

17 Apr        10.2   Multinomial Experiments, Goodness of Fit          p 546 # 1-11 odd

27 Apr        10.3   Contingency Tables                                                p 561 # 1-13 odd
28 Apr        11.2   One-Way Analysis of Variance                             p 583 # 1-9 odd

1 May         11.3   Two-Way Anaylsis of Variance                            p 598 # 1-7 odd
4 May             Practice Final Exam
5 May                 Review …

FINAL EXAM: Wednesday, 10 May 2000, 7:40-9:40 am