STA342 Statistical Theory II
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#### COURSE DESCRIPTION

This course builds on the calculus-based 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 p-values, goodness-of-fit 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 problem-solving 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 t-distribution 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 t-distributions)
• Derive and find confidence intervals for the difference of means (understanding when to use normal, and t-distributions)
• Derive and find confidence intervals for variances (using chi-square and F-distributions)
• Derive and find confidence intervals for proportions (understanding when to use normal, and t-distributions)
• 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 p-values) for
• Proportions
• One mean; equality of two means
• Equality of two normal distributions (understanding when to use normal, t-)
• Perform chi-square goodness-of-fit tests including contingency tables and one-factor 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 distribution-free 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, 5:00 P.M. - 6:15 P.M. Location: O'Hare 262.

## TEXTBOOK AND MATERIALS

• Required: Probability and Statistical Inference" 10th Edition by Robert V. Hogg, Elliot A. Tanis, and Dale Zimmerman. Pearson 2020.
• Strongly recommended: TI-83Plus or TI-84Plus graphing calculator. (Note: If calculators will be allowed on examinations, only the following models will be permitted: TI-83Plus, TI-84Plus.)

#### 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 fast-paced, 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: 1/28/2020