STAT 291 Statistics for the Mathematical Sciences I (3)

 Catalog Description:

Topics in probability and statistics: descriptive methods, conditional and unconditional probability, discrete and continuous distributions, one-sample estimation and hypothesis testing. Meets the General Education Mathematical Sciences requirement. (Offered fall semester only.)

 Prerequisites:

MATH 108 Intuitive Calculus with Applications or MATH 111 Calculus I with a C- or better

  1. Comfort with quantitative topics.
  2. Familiarity with summation notation and usage. This notation is used in both descriptive analysis and when working with discrete distributions.
  3. Understanding of elementary proofs.
  4. Ability to differentiate and integrate functions of one variable so that probabilities and moments can be considered for practical continuous distributions.
 Required Course Materials:

J. Devore, Probability and Statistics for Engineering and the Sciences, 8th edition, Cengage, 2012 (ISBN: 9780538733526)

 Course Coordinator:
 Course Audience:
    1. Students majoring in Mathematics, Mathematics-with-Certification, Physics, Physics-with-Certification.
    2. Students who select this course from a required menu majors in Computer and Information Science with Computer Science concentration, Economics (B.A.),
      Education-with-Certification (4-8) with Mathematics concentration, Education-with-Certification (4-8) with Science and Mathematics concentration, Nutrition Science.
    3. Students who select this course, a more mathematical introductory statistics course than STAT 269, to meet the General Education Mathematical Sciences requirement.
 Course Objectives:
    1. To become familiar with both descriptive and inferential analyses.
    2. To use probability in applied models and as the bridge between descriptive and inferential analysis.
    3. To intuitively understand each concept
    4. To understand when possible and appropriate, the rigor of a mathematical proof.
    5. To integrate topics by identifying commonalties.
    6. To understand the limitations of each analysis through consideration of assumptions.
    7. To express general concepts in terms of the application.
    8. To communicate results, clearly and completely, in a manner appropriate to nonquantitative audiences.
    9. To be introduced to the computer's capabilities in solving practical problems, using the computer for analysis only after understanding how to perform the analysis manually.

    General Education Objectives for the Mathematical Sciences Courses:

    1. To identify methods and assumptions of the mathematical sciences.
    2. To understand at least one of the three mathematical sciences of computing, mathematics, and statistics
      from a liberal arts perspective.
    3. To think logically, analytically, and abstractly through engagement in quantitative problem-solving
      activities.
 Topics:
    1. Descriptive Statistics: pictorial and tabular methods and measures of location and variability, and position.
    2. Probability: axioms and properties, counting techniques, conditional probability, and independence.
    3. Discrete Distributions: probability and moment calculations in general; binomial and Poisson distributions.
    4. Continuous Distributions: probability and moment calculations in general; normal, gamma (including exponential and chi-squared), and beta distributions.
    5. Sampling Distributions: Central Limit Theorem.
    6. One-Sample Interval Estimation: properties and assumptions; confidence intervals for a mean, proportion, and variance (standard deviation); sample size determination.
    7. One-Sample Hypothesis Testing: properties and assumptions; tests on a mean, proportion, and variance (standard deviation); power calculation; relationship to interval estimation; sample size determination.
 

Revised: October 2013; August 2011 (textbook)