## Rose-Hulman - Department of Mathematics - Course Syllabus MA223 - Engineering Statistics I - 2010-11

 Description & Prerequisites Course Goals Texts and Other Materials Course Topics Course Policies Links last posted to site: 08/19/10

Parts of the web page to be completed or determined by the instructor are in green.

Parts of the webpage not yet fully determined are in a red font.

### Catalogue Description and Prerequisites

MA 223 Engineering Statistics I 4R-0L-4C F, W, S Pre: MA 112 This is an introductory course in statistical data analysis. Topics covered include descriptive statistics, introduction to simple probability concepts, and random variables (including their linear combinations and expectations). The Central Limit Theorem will be presented. Hypothesis testing and confidence intervals for one mean, one proportion, and one standard deviation/variance will be covered as well as hypothesis testing and confidence intervals for the difference of two means. An introduction to one factor analysis of variance and simple linear regression will be presented. A computer package will be used for statistical analysis and simulation. Experimental data from a variety of fields of interest to the science and engineering majors enrolled will also be used to illustrate statistical concepts and facilitate the development of the student's statistical thinking.

Prerequisite: MA112 Calculus II

### Course Goals

• How to obtain or generate data.
• How to present data using various graphical methods.
• How to compute and interpret numerical summaries and graphical displays of data, both to answer questions and to check conditions (in order to use statistical procedures correctly).
• How to read articles that include statistical information.
• How and when to apply laws of probability and how these laws go hand-in-hand with statistical inference.
• How calculus and mathematics in general underlie the intuitive ideas behind both probability and statistics.
• The concept of a sampling distribution and how it applies to making statistical inferences based on samples of data.
• How to choose an appropriate statistical test for a given situation and/or parameter of interest.
• How to run a statistical test after verifying that conditions for those tests are met.
• How to make appropriate use of statistical inference.
• The concept of statistical significance including significance levels and p-values.
• How to communicate the results of a statistical analysis and communicate these results in context of the problem situation.
• How to apply modern technology and methods (e.g., bootstrapping) as an aid in descriptive and inferential statistics.
• How to apply statistical knowledge to various engineering applications.

### Textbook and other required materials

Textbook: Applied Statistics for Engineers and Scientists, 2nd edition -Jay Devore (Cal Poly) and Nicholas Farnum (Cal State Fullerton)
Computer Usage:  Minitab 15

### Course Topics

• Univariate and bivariate data visualization (histograms, side-by-side boxplots, scatterplots, times series plots, etc.)
• Univariate and bivariate descriptive statistics (mean, median, standard deviation, IQR, least squares line, correlation coefficient, etc.)
• Probability distributions (discussed from a calculus point of view), normal distribution, binomial distribution
• Sample spaces and events, probability laws, conditional probability and independence, simple system reliability
• Random variables (RV's): discrete and continuous RV's, linear combinations of RV's, and mean and variance of RV's
• Sampling (simple and stratified) and sampling distributions of various statistics, Central Limit Theorem
• Hypothesis testing: null and alternate hypotheses, type I and II errors, alpha, beta, power
• One-sample inference: point estimation, bias, confidence intervals and hypothesis tests of the population mean and proportion
• Two-sample inference: confidence intervals and hypothesis tests of the difference between two means, randomization
• Nonparametrics: bootstrap procedure and application to one-sample and two-sample inference
• K-sample inference: one-factor analysis of variance (ANOVA)
• Simple linear regression: estimation, hypothesis testing, confidence intervals, residual analysis

### Course Requirements and Policies

The following policies and requirements will apply to all sections and classes:

#### Computer Policy

A summary of the computer policy page:

Students will be expected to demonstrate a minimal level of competency with a relevant statistical package. The statistical package will be an integral part of the course and will be used regularly in class work, in homework assignments and during quizzes/exams. Students will also be expected to demonstrate the ability to perform certain elementary computations by hand. (See Performance Standards below.)

#### Performance Standards

Not yet specificed.

#### Final Exam Policy

The following is an extract from the final exam policy page. Consult the policy page for complete details.

The final exam will consist of two parts. The first part will be "by hands" (paper, pencil). No computing devices (calculators/computers) will be allowed during the first part of the final exam. This part of the exam will cover both computational fundamentals as well as some conceptual interpretation, though the level of difficulty and depth of conceptual interpretation must take into account that this part of the exam will be shorter than the second part of the exam.  No "cheat sheets", or prepared program on the calculator may be used. The second part of the exams will cover all skills: concepts, calculation, modeling, problem solving, and interpretation. Statistics tables, if needed, will be provided.