MATHS 181: Elementary Probability and Statistics (3)

MATH 181: Elementary Probability and Statistics (3 hours)Syllabus1. Prerequisite: Qualifying ACT or SAT score, or appropriate score on the mathematics placement test, orcredit in MATH 108, or permission of the department chairperson.2. Course Description: Algebra-based introduction to statistical applications through descriptive methods,probability, normal distributions, confidence intervals, hypotheses tests, regression and correlation.Misuses of statistics and common probability misconceptions are discussed. Statistical experiments andsimulations are conducted. Technology use is integrated throughout the course.3. Course Objectives: Students will develop an appreciation of the concepts of probability and randomnessand will understand how statisticians and scientists use data to make inferences and decisions. Studentswill be introduced to the key concepts of probability and of descriptive and inferential statistics.Students will:• Display, analyze, and interpret sample data using the techniques of exploratory data analysis;• Explore probability in random events• Represent relationships between variables with scatterplots, correlation, and simple linear regression;• Demonstrate appropriate use of technological tools for collecting, analyzing, and drawing conclusionsfrom data.4. Course Rationale: Statistics has become an increasingly important aspect of modern life. It is imperativethat the well-educated person has a basic understanding of statistical reasoning and how decisions are madein the face of uncertainty.5. Course Content: The following topics will be covered: descriptive methods such as measures of locationand dispersion, basic probability, the normal distribution, confidence intervals, hypotheses testing, simplelinear regression, correlation, and simulation.6. Course Format: The course will be taught through lecture and interactive discussion. Students will work insmall groups and will complete computer laboratory assignments which emphasize the analysis of results.7. Methods of Evaluating Student Performance: Course grades are determined primarily by studentperformance on tests and computer assignments, as well as quizzes, homework assignments, and classparticipation. Students are evaluated on content material and on their ability to communicate this materialto others orally and/or in writing. The evaluation and weight of these various components are at thediscretion of the instructor.8. Evaluation of the Course: The instruction of the course is evaluated by university and departmental studentevaluations and peer evaluations. The course is reviewed and revised periodically by the Department’sUndergraduate Programs Committee.9. Course text: Fundamentals of Statistics, 3 rd Edition, Michael Sullivan, III, Prentice Hall, 2011.10. The following schedule is offered. A day is meant to be a 50 minute class period. Adjustments are neededfor 75 minute class periods and summer sessions.

11.Section Topic Days1.1 The Practice of Statistics 11.2Observational Studies v. Designed Experiments11.3Simple Random Sampling1.4 Other Effective Sampling Methods 11.51.6Bias in samplingDesign of Experiments12.1 Organizing Qualitative Data 12.2 Organizing Quantitative Data 13.1 Measures of Central Tendency 13.2 Measures of Dispersion 13.3 Measures of Central Tendency & Dispersion from Grouped Data 13.4 Measures of Position & Outliers 13.5 Five-Number Summary & Boxplots 14.1 Scatter Diagrams and Correlation 14.2 Least-Squares Regression 14.3 Coefficient of Determination 15.1 Probability Rules 15.2 Addition Rule & Complements 15.3 Independence & the Multiplication Rule 15.4 Conditional Probability & the General Multiplication Rule 15.5 Counting Techniques 15.6 Putting It Together: Which Method Do I Use? 16.1 Discrete Random Variables 16.2 Binomial Probability Distribution 27.1 Properties of the Normal Distribution 17.2 Standard Normal Distribution 17.3Applications of the Normal Distribution17.4Assessing Normality7.5 Normal Approximation to the Binomial Probability Distribution 18.1 Distribution of the Sample Mean 18.2 Distribution of the Sample Proportion 19.1 The Logic in Constructing Confidence Intervals for a Population Mean When the Population Standard 1Deviation is Known9.2 Confidence Intervals for a population Mean When the Population Standard Deviation is Unknown 19.39.4Confidence Intervals for a Population ProportionPutting it Together: Which Procedure Do I Use?110.1Language of Hypothesis Testing110.2Hypothesis Tests for a Population Mean – Population Standard Deviation Known10.3 Hypothesis Tests for a Population Mean – Population Standard Deviation Unknown 110.410.511.111.2Hypothesis Tests for a Population ProportionPutting It Together: Which Method Do I Use?Inference about Two Means: Dependent SamplesInference about Two Means: Independent Samples1112.1Goodness-of-Fit Test112.2Tests for Independence & the Homogeneity of Proportions12.3 Testing the Significance of the Least-Squares Regression Model 112.4 Confidence and Prediction Intervals 139 daysReview3 daysExams3 daysTotal[January 2001, Pierce, E. Bremigan, Umbach; October 2005, Pierce; October 2010, Bergs; October 2012, UPC: R. Pierce, Chair]45 days