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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 Learning Outcomes
  1. Analyze data sets using graphical displays and numerical summaries. 
  2. Compute and interpret probabilities and conditional probabilities for discrete and continuous variables.
  3. Compute and interpret the mean, standard deviation, and variance of discrete and continuous random variables including the binomial and normal cases and the case of jointly distributed variables. 
  4. Compute point estimates and interval estimates for parameters.
  5. Formulate and conduct hypothesis tests for parameters.
  6. Apply appropriate statistical methods to solve real-world problems.
Major Topics/Skills to be Covered:
  • 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
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: 20

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: April 1, 2015
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 learning outcomes and cover the subjects listed in the Major Topics/Skills to be Covered section. 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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