Course Outline for Mathematics 43S
Introduction to Probability and Statistics with Support

Effective: Fall 2019
SLO Rev: 09/06/2018
Catalog Description:

MTH 43S - Introduction to Probability and Statistics with Support

5.00 Units

Descriptive statistics, including measures of central tendency and dispersion; elements of probability; tests of statistical hypotheses (one and two populations); correlation and regression; ANOVA; applications in various fields. Introduction to the use of computer software package to complete both descriptive and inferential statistics problems. This course is equivalent to MTH 43 with additional lab hours for students who did not place directly into MTH 43 or for students who place directly into MTH 43 but desire additional instruction. May not receive credit if Mathematics 35 has been completed. Laboratory, study group, collaborative workshop or computer laboratory time for Introduction to Probability and Statistics.
Strongly Recommended: ENGL 1A, Prerequisite: MTH 53 or MTH 53B or MTH 54 or MTH 54L or MTH 55 or MTH 55B or MTH 55L or an appropriate placement through the Mathematics Placement process.
1701.00 - Mathematics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 4.00 72.00 144.00 216.00
Laboratory 1.00 54.00 0.00 54.00
Total 5.00 126.00 144.00 270.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. Distinguish among different scales of measurement and their implications;
  2. Interpret data displayed in tables and graphically;
  3. Apply concepts of sample space and probability;
  4. Calculate the mean, median, mode, variance and standard deviation for a given data set;
  5. Identify the standard methods of obtaining data and identify advantages and disadvantages of each;
  6. Identify the sample(s) and population(s) in a data set description;
  7. Describe the basic principles of experimental design;
  8. Calculate probabilities of various independent or dependent events;
  9. Calculate the mean and variance of a discrete distribution;
  10. Calculate probabilities using normal and t-distributions;
  11. Describe the nature of the binomial distribution and normal distribution, as well as properties of the normal probability curve;
  12. Distinguish the difference between sample and population distributions and analyze the role played by the Central Limit Theorem;
  13. Construct and interpret confidence intervals;
  14. Determine and interpret levels of statistical significance including p-values;
  15. Interpret the output of a technology-based statistical analysis;
  16. Identify the basic concept of hypothesis testing including Type I and II errors;
  17. Formulate hypothesis test involving samples from one and two populations;
  18. Select the appropriate technique for testing a hypothesis and interpret the result;
  19. Use linear regression and ANOVA analysis for estimation and inference, and interpret the associated statistics;
  20. Use appropriate statistical techniques to analyze and interpret applications based on data from disciplines including business, social sciences, psychology, life science, health science, physical science, engineering and education;
  21. Read a question, write the appropriate mathematical symbols, utilize proper statistical language, and provide a coherent solution to problems used in Introduction To Probability and Statistics;
  22. Use technology currently available, such as calculators or statistical software programs, to appropriately solve problems in Introduction To Probability and Statistics;
  23. Solve problems independently and with peers, without having to rely on an instructor.
Course Content:
  1. Summarizing and analyzing data graphically and numerically
    1. Types of Data
    2. Levels/scales of measurement
    3. Frequency and relative frequency distributions
    4. Frequency and relative frequency histograms
    5. Five-number summaries and boxplots
    6. Scatter plots
    7. Two-way tables
    8. Measures of central tendency
      1. Mean
      2. Median
    9. Measures of dispersion
      1. Range
      2. Standard deviation
      3. Interquartile range
    10. Percentiles
    11. Empirical rule
  2. Experimental Design
  3. Probability
    1. Events and sample spaces
    2. Probability laws
    3. Independent and dependent events
  4. Random variables
    1. Expected value
    2. Distribution
      1. Uniform
      2. Binomial
      3. Normal
      4. Student t
      5. Chi-square
  5. Sampling and sampling distributions
  6. The Central Limit Theorem
  7. Estimation and confidence intervals
    1. One proportion z-interval
    2. One mean t-interval
  8. Hypotheses testing and inference
    1. One population proportion z-test
    2. One population mean t-test
    3. Two population difference of mean t-test
    4. Two population mean of difference t-test
    5. Chi-square tests
  9. Correlation and linear regression and analysis of variance (ANOVA)
  10. Applications using data from disciplines including business, social sciences, psychology, life science, physical sciences, engineering and education
  11. Statistical analysis using technology such as SPSS, JMP, Minitab
  12. Reflect on Study Skills
    1. Grit and Growth Mindset
    2. How Learning Math is Different
    3. Resources On and Off Campus
    4. Time Management
    5. How to Be an Effective Listener and Take Notes
    6. How to Approach Homework
    7. How to Study for an Exam
    8. Overcoming Math and Test Anxiety
  13. Review of Algebra Skills
    1. Operations with Fractions
    2. Order of Operations
    3. Evaluate Variable Expressions 
    4. Solving Linear Equations
    5. Soving Systems of Equations with Subsitituion 
    6. Dimensional Analysis
    7. Rates of Change
    8. Unit Ratios
    9. Calculate Slope
    10. Interpret Slope
    11. Graph Linear Equations
Methods of Instruction:
  1. Collaboration in small and/or large groups
  2. Graphing Calculator Instruction
  3. Individual Instruction
  4. Lecture/Discussion
  5. Problem Solving
  6. Class and group discussions
  7. Written assignments
  8. Group Activities
  9. Laboratory exercises
  10. Presentation of audio-visual materials
  11. Computer-based interactive curriculum
  12. Simulations
  13. Online Assignments
  14. Group Presentations
  15. Textbook reading assignments
  16. Self-reflection on course performance
  17. Student Participation
  18. Videos
Assignments and Methods of Evaluating Student Progress:
  1. Additional examples from outside sources, particularly, socially and culturally relevant examples: analyze graphs of income inequality, homelessness in the bay area, and systemic racism in the prison system.
  2. Enter the data on test scores into a Minitab worksheet. Create a histogram, stem-and-leaf diagram, and boxplot of the data. Calculate the mean, standard deviation, and five- number summary. Write a brief analysis of the data based on these graphical and numerical summaries.
  3. Determine the range and sample standard deviation of the tornado occurrence data in Exercise 3.43. Discuss one major drawback to the standard deviation as a measure of variation.
  4. Computer assignments using statistical software: Load a large data multivariate data file on test scores into statistical software. Create appropriate graphical displays and obtain summary statistics. Write a brief analysis of the data based on these graphical and numerical summaries.
  1. Quizzes
  2. Homework
  3. Midterm Examination
  4. Final Examination
  5. Laboratory exercises
  6. Projects
  7. Practical Examination
  8. Class Work
  9. Attendance
  10. Class Participation
  11. Study Skills Reflections
Upon the completion of this course, the student should be able to:
  1. Critically analyze mathematical problems using a logical methodology.
  2. Communicate mathematical ideas, understand definitions, and interpret concepts.
  3. Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Illowsky, Dean (2017). Introductory Statistics OpenStax.
  2. Davis, M (2015). Meaningful Statistics (5/e). Pearson Custom Publishing.
  3. Moore, Notz, Fligner (2015). The Basic Practice of Statistics (7/e). W.H. Freeman.
  4. Lock, Lock, Morgan, Lock and Lock (2015). Unlocking the Power of Data (2/e). Wiley.
  5. Weiss (2008). Elementary Statistics (7/e). Addison Wesley.
  1. R. R Core Team, (/e).
  2. StatCrunch. Pearson, (/e).
  • Graphing statistical calculator may be required.
  • Statistical software.
Abbreviated Class Schedule Description:
Descriptive statistics, including measures of central tendency and dispersion; elements of probability; tests of statistical hypotheses (one and two populations); correlation and regression; ANOVA; applications in various fields. Introduction to the use of computer software package to complete both descriptive and inferential statistics problems. This course is equivalent to MTH 43 with additional lab hours for students who did not place directly into MTH 43 or for students who place directly into MTH 43 but desire additional instruction. May not receive credit if Mathematics 35 has been completed.
Strongly Recommended: ENGL 1A, Prerequisite: MTH 53 or MTH 53B or MTH 54 or MTH 54L or MTH 55 or MTH 55B or MTH 55L or an appropriate placement through the Mathematics Placement process.