Math 200—Introduction to Statistics
Syllabus—Fall 2006

Catalog Description

This course is an introduction to the basic principles of statistics. Major topics include graphic, numeric, and algebraic summaries of data (graphs, measures of central tendency and spread, correlation and regression); elementary principles of sampling and experimental design; elementary probability; normal distributions and the central limit theorem; confidence intervals; and tests of significance. Focus on analysis of data using appropriate statistical techniques.
Prerequisites: MA 145 or placement

Rationale

This course is intended to provide the student with the basic tools of statistical analysis so that they can apply statistics in other courses or pursuits, satisfy admissions criteria for graduate programs, and become better-informed citizens. Since statistics are a central feature of our quest for understanding in the physical, biological, and social sciences, an introductory experience of this nature greatly enhances the student's potential for life-long learning.

Goals

At the conclusion of this course, the student will be able to:

1. Comprehend the basic principles and techniques of exploratory data analysis.
2. Comprehend and apply basic principles of probability.
3. Apply the normal distribution as a model for the distribution of random variables.
4. Apply common estimation and testing procedures.
5. Critically assess the design of sampling procedures and experiments.

Competencies

At the conclusion of this course the student will be able to:

1. Select and interpret graphic and numeric summaries for a single numeric variable. (Math SSC 1.01, 1.02, 1.10, 1.11, 4.1, 5.1, 7.2, 7.3)
   Performance indicators: Students will:
   • Choose appropriate graphic and numeric methods for summarizing data from a single variable and interpret the results accurately.
2. Use appropriate graphic and numeric summaries to compare the distribution of a measure across different groups. (Math SSC 1.01, 1.02, 1.10, 1.11, 4.1, 5.1, 7.2, 7.3)
   Performance indicators: Students will:
   • Choose appropriate graphic and numeric methods for comparing the distribution of a measure among different groups and summarize results and make valid conclusions.
3. Use scatterplots, correlation, and regression to explore and describe the relationship between two numeric variables. (Math SSC 1.01, 1.02, 1.10, 1.11, 4.1, 5.1, 7.3)
   Performance indicators: Students will:
   • Comprehend and appropriately use and interpret scatterplots, correlation, and regression in examining the relationship between two numeric variables.
4. Determine the probability of events using counting techniques, rules of probability, conditional probability, and the multiplication rule. (Math SSC 1.01, 1.02, 4.2)
   Performance indicators: Students will:
   • Utilize rules of probability and related techniques to accurately determine the probability of specific events.
5. Determine the mean and variance of a discrete random variable. (Math SSC 1.01, 1.02, 1.11, 4.1)
   Performance indicators: Students will:
   • Comprehend the concepts of mean and variance and correctly derive their respective values using calculators and/or software applications.
6. Assess the use of the normal distribution to model a numeric variable. Use normal distributions to calculate probabilities. (Math SSC 1.01, 1.02, 1.11, 4.1)
   Performance indicators: Students will:
   • Comprehend properties of the normal distribution and correctly determine probabilities from this distribution.
7. Assess the strengths and weaknesses of sampling procedures and experimental designs. (Math SSC 1.01, 1.02, 4.4)
   Performance indicators: Students will:
   • Given a specific example, choose appropriate sampling procedures and experimental designs for the production of "trustworthy" data.
   • Demonstrate knowledge of the advantages and disadvantages of various sampling procedures and experimental designs.
8. Use common estimation procedures. Interpret computer output. Discuss limitations of procedures and the meaning of confidence level. (Math SSC 1.01, 1.02, 1.11, 4.3)
   Performance indicators: Students will:
   • Choose and utilize appropriate estimation procedures and draw valid conclusions.
   • Comprehend the reasoning of inference and the limitations of confidence intervals and tests of significance.
9. Use common hypothesis tests. Interpret computer output, especially the meaning and significance of the p-value. Discuss limitations of procedures. (Math SSC 1.01, 1.02, 1.11, 4.3)
   Performance indicators: Students will:
   • In common hypothesis tests, assess the evidence against the null hypothesis in terms of probability.
   • Correctly interpret computer output and demonstrate understanding of p-value.
   • Delineate limitations of statistical tests used.

Course Information

Required Textbook

Moore, D. S. & McCabe, G. P. (2003). Introduction to the Practice of Statistics, (4^th ed.), New York: W. H. Freeman and Company.

Bibliography

Bordens, K. S. & Abbott, B. B. (1991). Research Design and Methods: A Process Approach, (2^nd ed.), Mountain View, California: Mayfield Publishing Company.

Berk, K. N. & Carey, P. (2004). Data Analysis with Microsoft Excel: Updated for Windows XP, Belmont, California: Brooks/Cole.

Isaac, S. & William, M. B. (1995). Handbook in Research and Evaluation for Education and the Behavioral Sciences, (3^rd ed.), San Diego: Robert R. Knapp, Publisher.

McIntyre, L. J. (2005). Need to Know: Social Science Research Methods, New York: McGraw-Hill.

Calculators and Computers

Although statistics is a mathematical science, it is not a field of mathematics. As such, this course emphasizes statistical ideas and conceptual understanding, not rigorous mathematical computations. The student is required to read and use equations, but is not expected to carry out statistical analyses step by step. Most statistical calculations and graphics can be produced through software and is done so in practice. Therefore, this course will require time on the computer using the statistical capabilities of Microsoft Excel at various times during the semester. A calculator with "two-variable statistics" capabilities is also helpful but not required. This calculator should have functions for correlation and least-squares regression as well as for the mean and standard deviation.

Course Requirements and Evaluation

Final grades will be determined by the percentage of possible points earned from exams, etc., according to the following scale:

Homework and Quizzes

Homework will be assigned on a regular basis. A homework assignment is worth 5 or 10 points (depending on length) if it is complete, accurate and turned in on time. Late homework will receive a maximum of 50% of the original credit. If you will be missing class on the date that an assignment is due, you must turn it in prior to the date or you must make arrangements with the professor. Each quiz is worth 10 points. Announcement of any upcoming quiz will be made in class. You cannot make up a missed quiz.

Laboratory exercises and writing assignments

Laboratory exercises will generally involve time on the computer. Instructions for laboratory exercises and topics for writing assignments will be given in class. Writing assignments are intended to help you organize your thoughts and clearly verbalize your understanding of statistical concepts. Points for exercises and labs vary. Late labs and assignments will receive a maximum of 50% of the original credit.

Exams

Exams will be announced. If you have a conflict, it is your responsibility to notify me as soon as possible. Make-up exams are only allowed for validated illnesses, emergencies, and college-related activities such as field trips or sporting events, where your name is on the list of excused students. You must contact me before the exam if you know you will miss the exam and arrange with me to take the make-up exam before the next class session. The exam grade will be discounted 10% for each class session thereafter. Extenuating circumstances will be treated on a case-by-case basis.

Attendance

Attendance is expected and required at each class meeting.

Any student who misses two consecutive weeks of class will be administratively withdrawn from class. If the withdrawal takes place within the first 6 weeks of class, the student will receive a grade of “W”. If the withdraw takes place after the 6^th week of class, the student will receive a “WF” or “WP”. The student will be notified of the action by the Registrar’s Office. Readmission will be considered only for extenuating circumstances as approved by the Vice President of Academic Affairs and Registrar. In such cases, where readmission is approved, a readmit fee of $350 will be charged. If a student drops below full-time status of 12 hours, financial aid may be adversely affected. Resident students dropping below 12 hours will be asked to move out of campus housing.

Note: If you know that you want to drop or withdraw from a class, please see your advisor. Do not count on this policy to automatically withdraw you.

Tentative Schedule

Final Exam: 1 p.m., Wednesday, December 6

You must take the final exam at the time designated for your class. The final exam is mandatory. Make your travel arrangements accordingly.