STAT 292 Statistics for the Mathematical Sciences II (3)

 Catalog Description:

Further topics in probability and statistics: two-sample estimation and hypothesis testing, analysis of variance, categorial data, simple and multiple linear regression, and nonparametric techniques. (Offered spring semester only.)

 Prerequisites:

    STAT 291 Statistics for Mathematical Sciences I

    1. Familiarity with basic statistical distributions.
    2. Understanding of one-sample estimation and hypothesis testing.
    3. Ability to use the computer to perform statistical analyses.
 Required Course Materials:

J. Devore, Probability and Statistics for Engineering and the Sciences, 7th edition, Brooks/Cole, 2008 (ISBN 0-495-38217-5)

 Course Coordinator:
 Course Audience:
    1. Students majoring in mathematics or computer science.
    2. Students wanting a more rigorous second statistics course.
    3. This course satisfies the second course statistics/computer science requirement for mathematics majors and can be used to meet the elective requirement for computer science majors.
 Course Objectives:
    1. To use probability as the bridge between descriptive and inferential analysis.
    2. To intuitively understand each concept.
    3. To understand, when possible and appropriate, the rigor of a mathematical proof.
    4. To integrate topics by identifying commonalties.
    5. To understand the limitations of each analysis through consideration of assumptions.
    6. To express general concepts in terms of the application.
    7. To communicate results, clearly and completely, in a manner appropriate to nonquantative audiences.
    8. To be introduced to the computer's capabilities in solving practical problems, using the computer for analysis only after understanding how to perform the analysis manually.
 Topics:
    1. Two-Sample Interval Estimation: properties and assumptions; confidence intervals for the difference between two means and proportions and the ratio of two variances (standard deviations); and sample size determination.
    2. Two-Sample Hypothesis Testing: properties and assumptions; tests on the difference between two means and proportions and the ratio of two variances (standard deviations); power calculations; relationship to interval estimation; and sample size determination.
    3. Analysis of Variance: properties and assumptions, one-way and partial and complete two-way ANOVA's, and multiple comparisons.
    4. Nonparametric Inference: two-sample estimation and hypothesis testing for the difference between two means.
    5. Simple Linear Regression: properties and assumptions, fitting the model by least squares, descriptive analysis, hypothesis tests, and confidence and prediction intervals.
    6. Linear Correlation Coefficient: properties and assumptions, descriptive analysis, hypothesis tests, confidence interval, and nonparametric hypothesis test.
    7. Multiple Linear Regression: properties and assumptions, fitting the model by least squares, descriptive analysis, hypothesis tests, confidence and prediction intervals, model building, standardized regression, and regression using dummy variables.
    8. Analysis of Categorical Data: test on multinomial proportions, goodness-of-fit test, and test of independence (test on the differences among two or more multinomial proportion vectors).
 

Revised: August 2010