Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 12H


COURSE DESCRIPTION
12H Honors Statistics Units: 3.00
 
Prerequisite(s): MAT 35: Intermediate Algebra
or qualifying placement level.

Limitation on Enrollment: Enrollment in the Honors Program.
A comprehensive study of measures of central tendency and variation, the normal distribution, the t-distribution, the chi-square distribution, linear correlation, testing of hypotheses, probability, and estimation. This Honors course offers an enriched experience for accelerated students through limited class size, seminar format, focus on primary texts, and application of higher-level critical thinking skills. Students may not receive credit for both MAT-12 and MAT-12H. 54 hours lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
Offers students in the Honors Program a study of statistical methods and their application to hypothesis testing and estimation of population parameters.
 
ADVISORY ENTRY SKILLS
Before entering the course, students will be able to:
  1. Apply the basic operations of algebra on the set of real numbers, polynomials, rational and radical expressions.

  2. Solve linear, rational, quadratic, exponential, and radical equations.

  3. Find terms of sequences and sums of series.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

Critique methods used to collect data.  Organize sets of data and calculate a variety of statistics for a given set of data (e.g. mean, median, variance).  Analyze data. 

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Construct sound arguments and evaluate arguments of others
  3. Critical Thinking - Recognize and assess evidence from a variety of sources
  4. Critical Thinking - Generalize appropriately from specific contexts
  5. Breadth of Knowledge - Understand the basic content and modes of inquiry of the major knowledge fields
  6. Breadth of Knowledge - Analyze experimental results and draw reasonable conclusions from them
  7. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  8. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Count the number of possible outcomes for various sequences of events, including permutations and combinations.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Recognize and assess evidence from a variety of sources

Use multiplication and/or addition rules to determine probabilities of events.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Determine the probability distribution for discrete random variables, including binomial random variables.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Determine and interpret confidence interval estimates for population means, proportions, and variances.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Perform hypothesis tests for one or two means, proportions, or variances.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Consider and evaluate rival hypotheses
  3. Critical Thinking - Generalize appropriately from specific contexts
  4. Critical Thinking - Integrate knowledge across a range of contexts
  5. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  6. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Calculate the Pearson product moment correlation coefficient and explain its significance.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Determine the regression equation and use it to make predictions, as appropriate.
   

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Recognize and assess evidence from a variety of sources
  3. Critical Thinking - Generalize appropriately from specific contexts
  4. Critical Thinking - Integrate knowledge across a range of contexts
  5. Breadth of Knowledge - Analyze experimental results and draw reasonable conclusions from them
  6. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  7. Application of Knowledge - Maintain and transfer academic and technical skills to workplace
 
COURSE CONTENT
  TOPICS
 
  1. Introduction to the meaning of statistics, abuses of statistics, and sampling methods
  2. Organizing data using tables and graphs
  3. Data summary and descriptions of important characteristics of data
  4. Counting and probability methods
  5. Probability distributions
  6. Normal probability distributions
  7. Interval estimates and determining sample size
  8. Testing hypotheses about population proportions, means, and variances
  9. Correlation and regression lines
  10. Chi-square tests and analysis of variance

Honors course will use a thematic approach to develop statistical concepts, rather than a topic based approach.
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  1. Class discussions and demonstrations of organizing data, counting, determining probabilities and probability distributions, estimating and hypothesis testing, and using the regression equation.
  2. Reading and writing activities designed to assist students in mastering the calculation of statistics, probabilities, and confidence intervals, as well as hypothesis testing.
  3. Employment of a variety of resources such as videos, slides, computer-based tools, manipulatives, and handouts in order to address individual learning styles and reinforce material.
  4. Small group activities in order to promote discovery and critical thinking.
  5. Peer review of student projects in order to develop and expose the ability to analyze statistics in a critical manner.

 Honors course will place special attention on activities that require critical thinking, reading and writing, student initiative, preparation, and participation, including class discussions, presentations, research, and group work.
 
METHODS OF EVALUATION
 Students will be evaluated for progress in and/or mastery of learning outcomes by methods of evaluation which may include, but are not limited to:

  • Written assignments designed to ensure the correct application of the methods used to analyze data and test hypotheses.
  • Quizzes and examinations designed to evaluate students’ calculations, estimates, hypothesis tests, and predictions.
  • Project designed to demonstrate the correct application of the methods used to collect, organize, and analyze data; then form conclusions based on the data.  Project should be equivalent to 20 pages of formal writing. 
  • Classroom participation in activities and discussions designed to ensure conceptual understanding of course content. 
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
COURSE MATERIALS
 All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include:

  • Triola, Mario F. . Essentials of Statistics. 2 ed. any: Addison Wesley, 2005.
  • Bluman, Allan G. . Elementary Statistics: A Step by Step Approach. 4 ed. any: McGraw-Hill, 2008.
  • Honors course will focus on articles from primary sources. Possible sources include, but are not limited to: The American Statistician, The Annals of Applied Probability, The Annals of Statistics, Journal of Applied Statistics, Statistical Computing & Graphics, and Statistical Science.
2007
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