# Project Examples

## Survey Statistics

Course: 22.361 - Applied Analysis, Mathematical Methods
Instructor: John McKelliget
Partner:SLICE Project

Partnership Description: Students in this course and s-l project applied statistics to the independent and dependent variables of the SLICE service-learning questionnaire for students to test relationships between variables and items on the survey. In this course and s-l project, students applied their knowledge of statistics to provide analysis and evaluation of questionnaire results. The first part of the survey inquired about general student demographics (independent variables). The second part of the survey inquired about student opinions relative to their s-l experience.

Project Description: Students selected independent variables that may have affected dependent variable outcomes. Since student distributions require sample sizes of less than 30, a random sample size, n = 18, was selected from each independent variable. A regression analysis was conducted to test best fit of the data. Consideration was given to selection of data points to be considered for inclusion in the regression, and what order the regression was performed. Mathematical methods were applied in a mechanical engineering context linked with service learning for an integrated analysis. Topics covered in this s-l project included: matrices and the solution of systems of linear algebraic equations, eigenvalues and eigenvectors, behavior of vectors and tensors under rotation of coordinate system, matrix approach to principal values and axes, iterative solution of non-linear equations, numerical integration and differentiation, regression analysis, and introduction to statistics and statistical inference.

### Learning objectives met by the S-L project were for students to:

• Determine whether one variable (dependent variable) is a function of another variable (independent variable)
• Postulate linear relationships to test experimental data points from LICE student surveys
• Selected five independent variables postulated to have an effect on dependent variables
• Conducted a linear regression for each set of data
• Calculated 95% confidence intervals in each data case
• Developed conclusions and produce a report expressing what was done, why this was done, and how conclusions were reached

### Community objectives met by the S-L project:

• Provided beginning analyses of SLICE data