College of Micronesia-FSM

MS 150 Statistics

Course Description: A semester course designed as an introduction to the basic ideas of data presentation, descriptive statistics, linear regression, and inferential statistics including confidence intervals and hypothesis testing. Basic concepts are studied using applications from education, business, social science, and the natural sciences. The course incorporates the use of a computer spreadsheet package for both data analysis and presentation. The course is intended to be taught in a computer laboratory environment.

Hours per week: 3
Number of weeks: 16
Semester credits: 3
Prerequisite course: MS 100 College Algebra

The order of the sections is not intended to reflect the chronological order of topics.

1. Mathematics Program Outcomes
   Students will be able to:
   • define arithmetic, algebraic, geometric, spatial, and statistical concepts
   • calculate arithmetic, algebraic, geometric, spatial, and statistical quantities using appropriate technology.
   • estimate arithmetic, algebraic, geometric, spatial, and statistical solutions
   • solve arithmetic, algebraic, geometric, spatial, and statistical expressions, equations, functions, and problems using appropriate technology.
   • represent mathematical information numerically, symbolically, graphically, verbally, and visually using appropriate technology.
   • develop mathematical and statistical models such as formulas, functions, graphs, tables, and schematics using appropriate technology.
   • interpret mathematical and statistical models such as formulas, functions, graphs, tables, and schematics, drawing conclusions and making inferences based on those models.
   • explore mathematical systems utilizing rich experiences that encourage independent, nontrivial, constructive exploration in mathematics.
   • communicate mathematical thoughts and ideas clearly and concisely to others in the oral and written form.
2. General Objectives
   Students will be able to:
   1. Calculate basic statistics (define, calculate)
   2. Represent data sets using histograms (define, calculate, estimate, represent)
   3. Solve problems using normal curve and t-statistic distributions including confidence intervals for means and hypothesis testing (define, calculate, solve, interpret)
   4. Determine and interpret p-values (calculate, interpret)
   5. Perform a linear regression and make inferences based on the results (define, calculate, solve, interpret)
3. Specific Objectives
   Students will be able to:
   
   Given one variable data and the use of a calculator or spreadsheet software on a computer
   
   
   1. Calculate basic statistics
      1. Distinguish between a population and a sample (define)
      2. Distinguish between a statistic and a parameter (define)
      3. Identify different levels of measurement when presented with nominal, ordinal, interval, and ratio data. (define)
      4. Determine a sample size (calculate)
      5. Determine a sample minimum (calculate)
      6. Determine a sample maximum (calculate)
      7. Calculate a sample range (calculate)
      8. Determine a sample mode (calculate)
      9. Determine a sample median (calculate)
      10. Calculate a sample mean (calculate)
      11. Calculate a sample standard deviation (calculate)
      12. Calculate a sample coefficient of variation (calculate)
   2. Represent data sets using histograms
      1. Calculate a class width given a number of desired classes (calculate)
      2. Determine class upper limits based on the sample minimum and class width (calculate)
      3. Calculate the frequencies (calculate)
      4. Calculate the relative frequencies (probabilities) (calculate)
      5. Create a frequency histogram based on calculated class widths and frequencies (represent)
      6. Create a relative frequency histogram based on calculated class widths and frequencies (represent)
      7. Identify the shape of a distribution as being symmetrical, uniform, bimodal, skewed right, skewed left, or normally symmetric. (define)
      8. Estimate a mean from class upper limits and relative frequencies using the formula Sx*P(x) here the probability P(x) is the relative frequency. (estimate)
   3. Solve problems using normal curve and t-statistic distributions including confidence intervals for means and hypothesis testing
      1. Discover the normal curve through a course-wide effort involving tossing seven pennies and generating a histogram from the in-class experiment. (develop)
      2. Identify by characteristics normal curves from a set of normal and non-normal graphs of lines. (define)
      3. Determine a point estimate for the population mean based on the sample mean (calculate)
      4. Calculate a z-critical value from a confidence level (calculate)
      5. Calculate a t-critical value from a confidence level and the sample size (calculate)
      6. Calculate an error tolerance from a t-critical, a sample standard deviation, and a sample size. (calculate)
      7. Solve for a confidence interval based on a confidence level, the associated z-critical, a sample standard deviation, and a sample size where the sample size is equal or greater than 30. (solve)
      8. Solve for a confidence interval based on a confidence level, the associated t-critical, a sample standard deviation, and a sample size where the sample size is less than 30. (solve)
      9. Use a confidence interval to determine if the mean of a new sample places the new data within the confidence interval or is statistically significantly different. (interpret)
   4. Determine and interpret p-values
      1. Calculate the two-tailed p-value using a sample mean, sample standard deviation, sample size, and expected population mean to to generate a t-statistic. (calculate)
      2. Infer from a p-value the largest confidence interval for which a change is not significant. (interpret)
   
   
   Given two variable data and the use of spreadsheet software on a computer
   
   
   5. Perform a linear regression and make inferences based on the results
      1. Identify the sign of a least squares line: positive, negative, or zero. (Define)
      2. Calculate the slope of the least squares line. (Calculate)
      3. Calculate the intercept of the least squares line. (Calculate)
      4. Solve for a y value given an x value and the slope and intercept of a least squares line. (Solve)
      5. Solve for a x value given an y value and the slope and intercept of a least squares line. (Solve)
      6. Calculate the correlation coefficient r. (Calculate)
      7. Use a correlation coefficient r to render a judgment as to whether a correlation is perfect, high, moderate, low, or none. (Interpret)
      8. Calculate the coefficient of determination r². (Calculate)

Course Intentions

• Use of Microsoft Excel and Microsoft Excel functions (or spreadsheet software with equivalent statistical functions) throughout the course as opposed to using dedicated statistics software package. Excel and other spreadsheets will be the desktop software most widely available to MS 150 students both while taking the course and, more importantly, in the workplace post-graduation.
• Use of real-world data, examples, and problems to the extent appropriate and possible.

Assessment

Assessment will be via quizzes, tests, midterm examinations and a final examination. All core outcomes will appear on the final examination.

Notes

The above format maps the course outcomes to the program outcomes using a reference in parentheses at the end of each outcome.

1. Textbook: Understanding Basic Statistics, Second Edition, Brase and Brase, Houghton Mifflin, 2001
2. Required course materials: In-class access to a computer with Microsoft Excel or spreadsheet software with equivalent statistical functions.
3. Reference materials
1. Microsoft Excel spreadsheet software by Microsoft or OpenOffice.org Calc software.
2. "Data Analysis with Microsoft Excel", Berk and Carey, Duxbury Press, 1998
3. "Statistics: A First Course", 6th ed. by Freund and Simon, Prentice Hall, Inc. 1995 (ISBN 0-13-083024-0),
4. "Elementary Statistics." 6th ed. by Johnson, PVVS-KENT Pub., 1992 (ISBN 0-534-92980-X)
4. Instructional costs: None anticipated at this time
5. Methods of Instruction: The course will be taught by lecture, class discussion, and the use of spreadsheet software for problem solving and computer simulations. This course will be taught in a computer laboratory classroom. Also, students will be encouraged to utilize the computer labs outside of class for homework assignments.
6. Evaluation: Homework, tests, quizzes, a midterm, and a final exam will be given. A standard 90%=A, 80%=B, 70%=C, 60%=D Below 60%=F grading scale is recommended.
7. Credit by examination: None
8. Attendance policy: As per the current college catalog

Appendix A

Further reading and background on the structure of this outline:
http://shark.comfsm.fm/~dleeling/department/slorevolution.html
http://shark.comfsm.fm/~dleeling/department/slorevolution_ii.html
http://shark.comfsm.fm/~dleeling/department/slorevolution_iii.html
http://shark.comfsm.fm/~dleeling/department/dnsm_program_outcomes.html
http://shark.comfsm.fm/~dleeling/department/slorevolution_v.html
http://shark.comfsm.fm/~dleeling/department/slorevolution_vi.html
http://shark.comfsm.fm/~dleeling/department/systemwidecompetencies.html http://shark.comfsm.fm/~dleeling/department/ms150goso.html
http://shark.comfsm.fm/~dleeling/department/ms150sidebyside.html