*[*

Approved by Faculty Senate.

University Studies Course Approval Proposal

Unity and Diversity – Critical Analysis

The Department of Mathematics and Statistics proposes the following course for inclusion in University Studies, Unity and Diversity, Critical Analysis at Winona State University. This was approved by the full department on Thursday, January 4, 2001.

Course: **Introduction to Engineering Statistics (STAT 303) 3 s.h.**

Catalog Description: Introduction to statistics and quality control concepts and techniques. Topics include graphical techniques, descriptive statistics, probability distributions, hypothesis testing, control charts, process capability studies, and additional topics in total quality management. This is a University Studies course satisfying requirements in Critical Analysis.

Prerequisite: MATH 160.

This is an existing course, previously approved by A2C2.

Department Contact Person for this course:

Joyce Quella; email wnquella@winona.edu

General Discussion of each objective in Critical Analysis as it relates to learning activities in STAT 303.

- evaluate the validity and reliability of information
- analyze modes of thought, expressive works, arguments, explanations, or theories
- recognize possible inadequacies or biases in the evidence given to support arguments or conclusions and
**advance and support claims**

Statistical techniques for estimating parameters, such as means, variances, correlation coefficients and regression parameters include consideration of validity and reliability. Validity and reliability are discussed in class and addressed in homework and tests.

Probability is used to compute likelihood of outcomes and analyze explanations and arguments. Probability distributions are used to model, explain and predict phenomena. Limitations of the models are also studied. Hypothesis tests for proportions, means and variances use probability theory to analyze arguments and claims. Constructing and analyzing arguments, explanations and theories are included in lecture, discussion, homework and tests.

Population parameters are estimated and assessed by adequacy. The binomial, Poisson and normal distributions are used to model phenomena, then assessed as to their adequacy. Correlation and other measures of association are found for bivariate data and then assessed for adequacy in describing the relation between the variables. Linear regression is used to describe and model bivariate data; then the regression models are assessed for adequacy. Control charts, based on binomial, Poisson and normal distributions, are used to describe processes and detect change in processes. The study of control charts includes limitations of use and probability of error. Hypothesis testing techniques for proportions, means and variances are studied and accompanied by consideration of the probability of making Type I and Type II as well as how to control the errors. All statistical techniques for estimation, inference and model building are accompanied by an assessment of their adequacy. The statistical techniques and assessment are included in homework, projects and tests.

Statistics 303 – Introduction to Engineering Statistics – 3 s.h.

**Course Description**: Introduction to statistics and quality control concepts and
techniques. Topics include graphical techniques, descriptive statistics, probability
distributions, hypothesis testing, control charts, process capability studies, and
additional topics in total quality management. This is a University Studies course
satisfying requirements in Critical Analysis.

Prerequisite: MATH 160.

**Possible Textbooks**:

Hogg, R. and Ledolter, J., __Applied Statistics for Engineers and Physical Scientists__,
2^{nd} ed., MacMillan Publishing Company, 1992. Walpole, R. and Myers, R__.,
Probability and Statistics for Engineers and Scientists__, 5^{th} ed., MacMillan
Publishing Company, 1993.

Unity and Diversity—Critical Analysis: Critical Analysis courses in the University Studies program are devoted to teaching critical thinking or analytic problem-solving skills. These skills include the ability to identify sound arguments and distinguish them from fallacious ones. The objective of these courses is to develop students’ abilities to effectively use the process of critical analysis. Disciplinary examples should be selected to support the development of critical analysis skills.

These courses must include requirements and learning activities that promote students’ abilities to

- evaluate the validity and reliability of information;
- analyze modes of thought, expressive works, arguments, explanations, or theories;
- recognize possible inadequacies or biases in the evidence given to support arguments or conclusions; and
- advance and support claims.

In the description of class topics and requirements below, these objectives in this list are referred to by a-d.

Topics Covered:

- Overview of Total Quality Management
- Descriptive statistics (a)

- Graphs for univariate and bivariate data
- Measured of central tendency
- Measures of variability
- Measures of relative standing

- Introductory probability (b,c,d)
- Important distributions (b,c,d)

- Binomial and Poisson distributions
- Normal distribution

- Sampling distributions (a)
- Estimation (a,c,d)

- Point estimation and desirable properties
- Interval estimation

- Common hypothesis testing situations and interval estimates (b,c,d)

- One sample proportion
- One sample test of the mean
- Two sample test of the mean – independent samples
- Two sample test of the mean – dependent samples
- Probability value

- Introduction to control charts (c)

- Statistical basis
- Types of charts

- X-bar
- R and S
- C and P
- CUSUM

- Introduction to process capability analysis

- Graphical
- Process capability ratios

- Design of experiments (b,c,d)

- Factorial designs

- Simple linear regression (c,d)

**Method of Instruction**: Lecture and discussion

**Evaluation Procedures**: Course requirements may include tests, homework assignments,
computer assignments, and projects. Students will be evaluated by their performance on
these assignments. (a,b,c,d)

**Approval/Disapproval Recommendations**

Department Recommendation: Approved Disapproved Date

Chairperson Signature Date

Dean's Recommendation: Approved Disapproved Date

Dean's Signature Date

*In the case of a Dean's recommendation to disapprove a proposal, a written rationale for the recommendation

to disapprove shall be provided to USS.

USS Recommendation: Approved Disapproved Date

University Studies Director's Signature Date

A2C2 Recommendation: Approved Disapproved Date

A2C2 Chairperson Signature Date

Faculty Senate Recommendation: Approved Disapproved Date

FA President's Signature Date

Academic VP's Recommendation: Approved Disapproved Date

VP's Signature Date

President's Decision: Approved Disapproved Date

President's Signature Date