Discipline: Mathematics
Originator: Rosalia Cueto

Riverside Community College District
Integrated Course Outline of Record

Mathematics 12
MAT-12 : Statistics
College:
Lecture Hours: 72.000
Outside-of-Class Hours: 144.000
Units: 4.00
Grading Methods: Pass/No Pass
Letter Grade
Course Description
Prerequisite: MAT-35 or MAT-37 or MAT-42 or qualifying placement level.
Course Credit Recommendation: Degree Credit

A comprehensive study of measures of central tendency and variation, correlation and linear regression, probability, the normal distribution, the t-distribution, the chi-square distribution, estimation, testing of hypotheses, analysis of variance, and the application of statistical software to data, including the interpretation of the relevance of the statistical findings. Applications using data from business, education, health science, life science, psychology, and the social sciences will be included. 72 hours lecture. (Letter Grade, or Pass/No Pass option.)
Short Description for Class Schedule
A study of statistical methods and their application to estimation of population parameters and hypothesis testing.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
  1. Apply the basic operations of algebra on the set of real numbers, polynomials, rational and radical expressions.
    • MAT-35 - Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.
    • MAT-37 - Demonstrate numerical, algebraic, and geometric reasoning skills to support statistical analysis.
    • MAT-42 - Simplify numerical, algebraic and linear expressions using correct mathematical symbols and language.
  2. Solve linear, absolute value, and radical equations.
    • MAT-35 - Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.
    • MAT-37 - Demonstrate numerical, algebraic, and geometric reasoning skills to support statistical analysis.
    • MAT-42 - Apply and identify appropriate methods to solve linear equations, quadratics equations, literal equations and inequalities in one and two variables.
  3. Solve inequalities in one variable.
    • MAT-37 - Demonstrate numerical, algebraic, and geometric reasoning skills to support statistical analysis.
    • MAT-42 - Apply and identify appropriate methods to solve linear equations, quadratics equations, literal equations and inequalities in one and two variables.
  4. Graph equations of lines and basic functions.
    • MAT-35 - Graph linear and basic nonlinear functions.
    • MAT-37 - Construct, use, and interpret mathematical models, specifically linear models to represent relationships in quantitative data and normal probability models to identify unusual events for a quantitative variable.
    • MAT-42 - Graph linear and basic non linear functions (by hand and using technology)
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Interpret data displayed in tables and graphically.
  2. Apply concepts of sample space and probability.
  3. Calculate measures of central tendency and variation for a given data set.
  4. Identify the standard methods of obtaining data and identify advantages and disadvantages of each.
  5. Calculate the mean and variance of a discrete distribution.
  6. Calculate probabilities using normal and t-distributions.
  7. Distinguish the difference between sample and population distributions and analyze the role played by the Central Limit Theorem.
  8. Construct and interpret one and two sample confidence intervals.
  9. Determine and interpret levels of statistical significance using traditional method and p-values.
  10. Interpret the output of a technology-based statistical analysis.
  11. Identify the basic concept of hypothesis testing including Type I and II errors.
  12. Formulate hypothesis tests involving samples from one and two populations
  13. Select the appropriate technique for testing a hypothesis and interpret the result.
  14. Use regression lines and ANOVA for estimation and inference, and interpret the associated statistics.
  15. Use appropriate statistical techniques to analyze and interpret applications based on data from at least four of the following disciplines: business, economics, social science, psychology, political science, administration of justice, life science, physical science, health science, information technology, and education.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Distinguish among standard methods of collecting data and interpret data displayed in tables and graphically.
  2. Calculate measures of central tendency and variation for continuous and discrete data sets.
  3. Calculate and interpret probabilities for normal distributions.
    • Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
    • Information Competency & Technology Literacy: Students will be able to use technology to locate, organize, and evaluate information. They will be able to locate relevant information, judge the reliability of sources, and evaluate the evidence contained in those sources as they construct arguments, make decisions, and solve problems.
  4. Construct and interpret confidence intervals.
    • Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
  5. Formulate hypotheses from samples from one, two or more populations, select the appropriate technique and interpret the results by using the traditional or the p-value method.
    • Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
    • Information Competency & Technology Literacy: Students will be able to use technology to locate, organize, and evaluate information. They will be able to locate relevant information, judge the reliability of sources, and evaluate the evidence contained in those sources as they construct arguments, make decisions, and solve problems.
Course Content:
  1. Levels of measurement
    1. Nominal, ordinal, interval, and ratio
  2. Organizing data using tables and graphs
    1. Frequency distributions
    2. Histograms
    3. Boxplots
  3. Descriptive statistics
    1. Measures of central tendency
    2. Measures of variation
    3. Measures of relative position
  4. Probability methods
    1. Sample Spaces
    2. Addition rule
    3. Complements
    4. Multiplication rule
  5. Random variables and expected value
  6. Sampling
    1. Sampling methods
    2. Sampling distributions 
  7. Binomial distributions
    1. Probabilities
    2. Mean and standard deviation
  8. Normal distributions
    1. Probabilities
    2. The Central Limit Theorem
  9. Confidence Interval estimates and determining sample size
    1. Proportion
    2. Mean
    3. Variance
  10. Hypothesis testing and inference
    1. z-tests for one and two populations
    2. t-tests for one and two populations
    3. Chi-square tests
  11. Correlation and linear regression
  12. Analysis of variance
  13. Technology-based statistical analysis using Minitab, Excel, StatCrunch, StatDisk,R, SPSS, SAS or the graphing calculator. 
  14. Applications using data from at least four of the following disciplines: business, economics, social science, psychology, political science, administration of justice, life science, physical science, health science, information technology, and education.
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
  • Class lectures, discussions, and demonstrations of interpreting data, determining probabilities, estimating and hypothesis testing, and the use of linear regression analysis.
  • Drills and pattern practices to assist students in mastering the calculation of statistics, probabilities, and confidence intervals, as well as hypothesis testing.
  • Employment of a variety of resources such as videos, slides, computer-based tools, manipulatives, and handouts in order to address multiple learning styles and reinforce material.
  • Small group activities in order to promote discovery and enhance problem solving skills.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
  • 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 inferences.
  • Projects designed to demonstrate the correct application of the methods used to collect, organize, and analyze data. 
  • Classroom activities and discussions designed to ensure conceptual understanding of course content.
Sample Assignments:
Outside-of-Class Reading Assignments
  • Read text, examples, and notes covering topics such as probability distributions and linear regression.
Outside-of-Class Writing Assignments
  • Interpret confidence interval estimates.  Perform hypothesis tests.
Other Outside-of-Class Assignments
  • Problem sets that require students to calculate measures of central tendency, measures of variation, and probabilities. 
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 the following:
  • Barbara Illowsky,‎ Susan Dean. Introductory Statistics . Open Stax College, 2017.
  • Bluman, A.G.. Elementary Statistics: A Step by Step Approach. 10 McGraw-Hill, 2017.
  • Charles A. Dana Center. Statistical Reasoning. 1 Pearson, 2016.
  • Triola, M.F. . Essentials of Statistics. 6 Addison Wesley, 2019.
Codes/Dates:
CB03 TOP Code: 1701.00 - Mathematics, General
CB05 MOV Transfer Status: Transfers to Both UC/CSU (A)
CB05 NOR Transfer Status: Transfers to Both UC/CSU (A)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
C-ID#: SOCI 125; MATH 110
Board of Trustees Approval Date: 12/11/2018
COR Rev Date: 12/11/2018