COURSE DESCRIPTION
This course builds on the calculusbased treatment of probability provided in
STA341 to introduce concepts in statistics. After studying additional topics in
probability (including Chebyshev's inequality and convergence in probability),
students study descriptive statistics; point estimation including unbiased,
maximum likelihood, method of moments, efficient and minimum variance estimators;
confidence intervals; tests of hypotheses, significance testing with pvalues,
goodnessoffit tests; analysis of variance; and nonparametric methods.
GENERAL COURSE GOALS
To have students:
 expand their understanding of the nature of mathematical statistics
 improve their mathematical problemsolving skills, including their skill in presenting rigorous mathematical arguments in proofs and derivations
 learn to use mathematical statistics to gain insight into areas of application, for example in the physical and life sciences, and economics
 appreciate the importance of statistics in human civilization
 learn the appropriate use of technology including how to use it and when to be skeptical of its results
 develop critical thinking and a basic understanding of logic essential for lifelong learning
SPECIFIC COURSE LEARNING OUTCOMES
By successfully completing this course, students should be able to:
 Use the Normal distribution to approximate discrete distributions, especially for binomial and Poisson.
 Describe the Student's tdistribution and solve associated probability problems
 State the idea estimation (of unknown parameters of distributions)
 Find point estimators
 Determine if a given point estimator is
 Unbiased
 Sufficient
 Efficient
 Minimum variance unbiased estimator
 Derive maximum likelihood estimators
 Derive methods of moments estimators
 Discuss the idea behind confidence intervals
 Derive confidence intervals using the pivotal method
 Derive and find confidence intervals for means (understanding when to use normal, and tdistributions)
 Derive and find confidence intervals for the difference of means (understanding when to use normal, and tdistributions)
 Derive and find confidence intervals for variances (using chisquare and Fdistributions)
 Derive and find confidence intervals for proportions (understanding when to use normal, and tdistributions)
 Find appropriate sample sizes related to finding confidence intervals at given confidence levels
 Derive (or at least justify steps in the derivation of) a simple (linear) regression problem
 State the main ideas behind tests of hypotheses
 Compute type I and type II errors
 Perform tests of hypotheses (using critical regions and pvalues) for
 Proportions
 One mean; equality of two means
 Equality of two normal distributions (understanding when to use normal, t)
 Perform chisquare goodnessoffit tests including contingency tables and onefactor analysis of variance (as time permits)
 Find the power of a statistical test (as time permits)
 Understand order statistics and their distributions (as time permits)
 Understand and find distributionfree confidence intervals for percentiles (as time permits)
 Understand and find use the Wilcoxon Tests (as time permits)
 Additional topics, as time permits.
SUPPORT OF THE UNIVERSITY MISSION
This course supports the mission of the university as follows: "...through teaching ... prepares men and women for
responsible lives by imparting and expanding knowledge, developing skills, and cultivating enduring values.
... students develop their abilities for thinking clearly and creatively,
enhance their capacity for sound judgment, and prepare for the challenge of learning throughout their lives."
PREREQUISITES
STA341 or equivalent.
WHERE AND WHEN
 Secion 01 : Course meeting time/place: M, W, 4:30 P.M.  5:45 P.M. Location: O'Hare 117.
TEXTBOOK AND MATERIALS
 Required: Probability and Statistical Inference" 9th Edition
by Robert V. Hogg, Elliot A. Tanis, and Dale Zimmerman. Pearson 2015.
 Strongly recommended: TI83Plus or TI84Plus graphing calculator.
(Note: If calculators will be allowed on examinations, only the following models will be permitted: TI83Plus, TI84Plus.)
TEACHING METHODOLOGY
Lecture, question and answer, readings, homework exercises.
GENERAL REMARKS AND ADVICE
This web site is designed to, among other things, make it clear what is expected from you and what you can expect from the
course and from me. This course will be challenging; it is fastpaced, it requires a great deal of meticulous attention to detail as well as imagination and creativity, and just about everything in it depends
on your understanding of everything else in the course that preceded it. Nevertheless, if you work hard,
do not allow yourself to fall behind, and seek help when you need it, you should be successful in this course.
Reading assignments and homework problems for nearly each class meeting are posted on the course web site.
It is your responsibility to check the web site frequently (i.e., at least once a day) for the homework.
It is extremely important that you complete the reading assignments and try the homework problems before the following class meeting.
Last modified: 1/16/2018
