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MAT 135

I.    TITLE: Introduction to Probability and Statistics

II.   CATALOG DESCRIPTION:
Elementary probability, the binomial, normal, student's and chi-square distributions, random sampling, regression and correlation.

III.  PURPOSE:
Statistical methods provide important tools for decision making in fields as diverse as law,  medicine, sociology and agriculture. No single course can make a student proficient in  statistics. The purpose of this course is to give the student an understanding of common  methodologies that are critical to quantitative investigations in these diverse fields. Students  preparing for careers in these  disciplines need the capacity to critically evaluate the current  research and literature  which incorporate the concepts and language of probability and  statistics. This  course will introduce students to those core concepts and enable them to  become conversant in the language of probability and statistics.

IV.  COURSE OBJECTIVES:
Many disciplines gather data in the context of an investigation and then use that data as the basis for making a decision or drawing a conclusion. It is the objective of this course  to give students the tools that will enable them to understand and appreciate the role probability and statistics plays in this process. They will study concepts important to data gathering such as experimental design, random sampling and sampling variability. They will learn and implement strategies for summarizing and displaying data in ways that aid the investigator in drawing conclusions. Concepts like measures of central tendency, dispersion and correlation will be applied to a variety of examples from different disciplines. The role of probability in quantifying the uncertainty in the decision process will be emphasized. Students will learn elementary probability concepts through problem solving. Classical probability distributions like the binomial and normal distributions will be studied in the context of applications where they are the appropriate tools for analysis. Formal inference procedures such as confidence intervals and hypothesis testing will be presented as general strategies for making decisions. The role of probability in the decision process will be stressed. Understanding and implementing these strategies in a few common settings( e.g. the t-test for a mean ) will be emphasized over learning a cookbook menu of specific procedures for a list of specific applications.

V.  CONTENT OUTLINE:
A. Describing and summarizing data
  a. Graphical methods: stemplots, histograms, boxplots, etc.
  b. Numerical methods: mean, median, standard deviation, percentiles
B. Relationships in data
  a. Correlation
  b. Linear regression, least squares principle
  c. Categorical data, contingency tables
C. Producing data
  a. Experimental Design, randomization
  b. Sampling, random samples
  c. Sampling variability and bias

D. Probability concepts
  a. Sample spaces and events
  b. Random variables and probability distributions
  c. Binomial distribution
  d. Normal distribution
  e. Sampling distributions
E. Inference
  a. Confidence intervals
  b. Hypothesis testing- general strategy
  c. Applications
   1) One sample-means and proportions
   2) Two sample-means and proportions
   3) Contingency tables-chi square test

VI.  INSTRUCTIONAL ACTIVITIES
The primary mode of instruction is the classroom lecture augmented by selections from a series of professionally produced videos which were designed to accompany the current text book. When appropriate, students work on exercises during class as reinforcement and practice for some concepts presented in lecture. For example, students might be asked to find the correct least squares regression line to fit a data set that has been presented. These classroom exercises may be appropriate for individual or group work. Regular homework quizzes are used to monitor progress in that area. Statistical calculators are recommended for the course to minimize time spent on computation.
It is expected that students in this class will exercise critical thinking in solving  statistical problems and then interpret the solutions in non-statistical language. For  example, an experimental problem may be assigned where the objective is stated in  non- statistical terms.
 The student would be expected to:
  1. Reformulate the objective of the experiment in terms of a statistical      problem.
  2. Determine appropriate statistical methodology to solve the problem.
  3. Correctly implement that methodology and interpret the results.
  4. Communicate the results, in writing, in non statistical language.

VII.    FIELD AND CLINICAL ACTIVITIES:   none

VIII.  RESOURCES:
 Along with the text, the video series Against All Odds: Inside Statistics ( 26 half-hour
 programs ), produced by the Consortium for Mathematics and It's Applications, is
 available for use in the classroom. Copies are also available in the Science Resource
 Center for student use outside of the class.

IX.  GRADING PROCEDURES
The course grade is based on three hourly exams, a two-hour comprehensive final exam, and an evaluation of homework. In hourly exams a student is expected to  demonstrate problem solving skills through written solutions of problems relevant to  the material covered. Students must show in writing, a logical process followed to a  correct answer to receive full credit. Partial credit is assigned to the extent that the  student  followed a correct process even though a minor error in logic or an arithmetic error may  lead too an incorrect answer. The three written exams constitute 50-70% of the final course  grade.  The actual weight depends on the instructor.
In the comprehensive final exam students must demonstrate an understanding of the  course  material by responding to written short answer questions and by solving  problems that  cover core concepts of the course. Again the process of solution is  evaluated as well as the answer. The final exam constitutes 20-30% of the course  grade.  The homework component counts 10-30% of the course grade.  Homework is typically  checked by the use of quizzes. A group project is generally included as part of the  homework component. Experimental data is analyzed and evaluated using one or more of  the methods covered in the course. Results are presented in a written report which includes  graphical interpretation of the data.
Grades are assigned according to the following scale:
  A  90-100
  B  80-89
  C  70-79
  D  60-69
  E  below 60

X. ATTENDANCE POLICY:
Regular class attendance is expected, especially for first year students. Attendance is monitored by some method determined by individual instructors.

XI. HONESTY POLICY
Any instance of academic dishonesty, as determined by the instructor ( in compliance with the Board of Regents Policy on Academic Integrity - Feb. 1975 ) will result in zero points for the assignment, or a grade of E for the course.

XII. TEXT AND REFERENCE:
Current

XIII.  PREREQUISITES:
ACT mathematics standard score of at least 20 or MAT 105

Last updated February 14, 2000. Designed and maintained by Kyosung Koo