Course Outline for Mathematics 43
Introduction to Probability and Statistics

Effective: Fall 2022
SLO Rev: 10/27/2021
Catalog Description:

MTH 43 - Introduction to Probability and Statistics

4.00 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. May not receive credit if Mathematics 35 has been completed.
Prerequisite: MTH 53 or MTH 55 or an appropriate skill level demonstrated through the Mathematics Assessment process. Strongly Recommended: Eligibility for ENGL 1.
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 0.00 18.00 0.00 18.00
Total 4.00 90.00 144.00 234.00
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.
Course Content:
  1. Summarizing and analyzing data graphically and numerically
    1. Sample vs population data
    2. Types of Data
    3. Levels/scales of measurement
    4. Frequency and relative frequency distributions
    5. Frequency and relative frequency histograms
    6. Five-number summaries and boxplots
    7. Scatter plots
    8. Two-way tables
    9. Measures of central tendency
      1. Mean
      2. Median
    10. Measures of dispersion
      1. Range
      2. Standard deviation
      3. Interquartile range
    11. Percentiles
    12. Empirical rule
  2. Study Design
    1. Experiment vs observational study
    2. Elements of an experiment
    3. Sampling methods
  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. Type I and II errors
    2. Statistical vs practical significance
    3. One population proportion z-test
    4. One population mean t-test
    5. Two population difference of mean t-test
    6. Two population mean of difference t-test
    7. Chi-square tests
  9. Linear regression
    1. Correlation
    2. Coefficient of determination
    3. Least squares regression line
  10. Analysis of variance (ANOVA)
  11. Applications using data from disciplines including business, social sciences, psychology, life science, physical sciences, engineering and education
  12. Statistical analysis using technology such as SPSS, JMP, Minitab
Methods of Instruction:
  1. Lecture/Discussion
  2. Class and group discussions
  3. Written assignments
  4. Group Activities
  5. Laboratory exercises
  6. Presentation of audio-visual materials
  7. Computer-based interactive curriculum
  8. Simulations
  9. Online Assignments
  10. Group Presentations
  11. Distance Education
  12. Problem solving
  13. Student participation
  14. Videos
Assignments and Methods of Evaluating Student Progress:
  1. 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.
  2. Enter the data on test scores into a statistical analysis package. Create relevant summary statistics, histogram, and boxplot of the data. Write a brief analysis of the data based on these graphical and numerical summaries.
  3. Using the data provided, compare the rates of depression between those firefighters who participated in 9/11 rescue and those who did not. Is the difference statistically significant? Include in your response any output you obtain from technology.
  1. Quizzes
  2. Homework
  3. Midterm Examination
  4. Final Examination
  5. Projects
  6. Practical Examination
  7. Lab Activities
Upon the completion of this course, the student should be able to:
  1. critically analyze mathematical problems critically 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. Moore, D., W. Notz, M. Fligner (2021). The Basic Practice of Statistics (9th). Macmillan.
  2. Lock, R., P. Lock, K. Morgan, E. Lock, D. Lock (2020). Statistics: Unlocking the Power of Data (3rd). Wiley.
  3. Illowsky, B., S. Dean (2021). Introductory Statistics OpenStax.
  • Statistical software.
  • Graphing statistical calculator may be required.
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. May not receive credit if Mathematics 35 has been completed.
Prerequisite: MTH 53 or MTH 55 or an appropriate skill level demonstrated through the Mathematics Assessment process. Strongly Recommended: Eligibility for ENGL 1.
Discipline:
Mathematics*