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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 338
Course Title: Mathematical Statistics and Probability
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description:

A calculus-based introduction to statistical methods dealing with basic probability, distribution theory, confidence intervals, hypothesis tests and sampling. Prerequisite: MATH 222 or MATH 235.

Prerequisite(s) / Corequisite(s):

MATH 222 or MATH 235.

Course Rotation for Day Program:

Offered odd Spring.

Text(s): Most current editions of the following:

Mathematical Statistics with Applications. 7th Edition
By Wackerly, Mendenhall, and Scheaffer
Probability and Statistics for the Engineering and Sciences
By Devore, Jay (Duxbury Press)
Course Objectives
  • To choose appropriate statistical methods to solve real-world problems and understand the limitations of the methods in making predictions and drawing conclusions.
  • To use appropriate technology to solve statistical problems.
  • To organize data, communicate the essential features of the data, and interpret data in meaningful ways.
  • To understand the role of probability in the foundation of modern statistical methods.
  • To utilize calculus to assist in the understanding and calculations of statistical quantities.
Measurable Learning
  • Classify data as qualitative or quantitative (discrete or continuous).
  • Identify advantages and disadvantages of sampling and common sampling methods.
  • Construct frequency distributions for qualitative data and frequency distributions, histograms, stem-and-leaf plots, and boxplots for quantitative data.
  • Use calculus to perform calculations involving continuous probability distributions.
  • Describe distributions of quantitative data in terms of shape, center and spread.
  • Compute probabilities using the addition rule, the multiplication rule, complements and counting techniques.
  • Determine if events are independent using conditional probabilities.
  • Construct discrete probability distributions.
  • Compute and interpret the mean (expected value) and standard deviation of a discrete random variable.
  • Compute probabilities of binomial experiments.
  • Compute probabilities and percentile values for normally distributed random variables.
  • Determine if a distribution is normally distributed.
  • Describe and explain the concept of a sampling distribution and of the Central Limit Theorem.
  • Compute point estimates and interval estimates for means and proportions.
  • Calculate and interpret estimators using the methods of Maximum Likelihood and of Moments.
  • Determine the sample size necessary for estimating a mean or proportion to within a given margin of error.
  • Test hypotheses for means or proportions using P values.
  • Test hypotheses and construct interval estimates for two population situations.
  • Perform and interpret Analysis of Variance tests.
  •  Interpret the method of linear regression.
Topical Outline:
  • Overview and descriptive statistics
  • Measures of location and variability
  • Sample spaces and events
  • Probability
  • Distributions of discrete and continuous random variables
  • Expected values
  • Normal distribution
  • Jointly distributed random variables
  • Statistics, sampling distributions and the Central Limit Theorem
  • MLEs and MMEs
  • Point estimation
  • Confidence intervals
  • Hypothesis testing
  • Two populations tests
  • Linear regression
Culminating Experience Statement:

Material from this course may be tested on the Major Field Test (MFT) administered during the Culminating Experience course for the degree. 
During this course the ETS Proficiency Profile may be administered.  This 40-minute standardized test measures learning in general education courses.  The results of the tests are used by faculty to improve the general education curriculum at the College.


Recommended maximum class size for this course: 30

Library Resources:

Online databases are available at You may access them from off-campus using your CougarTrack login and password when prompted.

Prepared by: Suzanne Tourville Date: November 6, 2013
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.

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