MATHEMATICAL MODELING
Mathematical Modeling Problems
Mathematical Modeling Data Excel
PERIOD THREE FINAL LINKS
FUTURE SPRING SEMESTER PROJECT OPTIONS
Spring Project #1 DUE WEDNESDAY January 16, 2013
Using Excel 2010 & The Normal Distribution
On Thursday, we reviewed calculating probability from normal population and sampling distributions. We learned how to draw a normal curve using Excel, and then shade a given probability region. This Excel workbook was examined in class. Its six worksheets sequentially guide students through the process of drawing a normal curve with Excel, shading a probability region, and fully labeling the resulting diagram..
Drawing A Normal Distribution And Shading A Probability Region
For those who do not have access to Excel 2010 at home, the following series of PDFs reproduce the six instructional worksheets.
PDF #1 PDF #2 PDF#3 PDF #4 PDF #5 PDF#6
Project #1 Instructions: Students will create two displays that graphically communicate:
(1) The characteristics of the distribution (center, shape, and spread), and
(2) Probability as a shaded region. This region would reflect the portion of the normally shaped sample set that matches a given event described in an inequality statement.
One of these displays will involve a sampling distribution, and the other one involves a population distribution. Students will use two probability statements assigned from the Fall Semester final reproduced below.
FALL FINAL QUESTIONS: BE SURE TO DO THE TEST & #s ASSIGNED IN CLASS
Grading of this project will consider:
Proper Mechanics (70%+/-); and
Creativity/Aesthetics That Enhance Communication (30%+/-)
ASSIGNMENT #1: DUE Friday January 25, 2013
Observational Study Design Glossary Assignment
Students will create a custom glossary by copying the definitions of terms from the two links below. The list of terms to be included in the Glossary are provided in the first posted document below. Understanding these terms will be critical when students soon begin designing their own sampling surveys. These terms and symbol notations will comprise the majority of the vocabulary section of the first spring midterm. ALL GLOSSARIES MUST BE HANDWRITTEN, & TERMS NUMBERED AS SHOWN . THE GLOSSARY SHOULD BE ORGANIZED IN OUTLINE FORM AS SHOWN IN THE "LIST OF TERMS".
LIST OF TERMS TO BE INCLUDED IN GLOSSARY
Stat Trek Survey Sampling Source: stattrek.c0m
Additional Survey Terms Source: sciencebuddies.org
ASSIGNMENT #2: DUE Thursday January 24, 2013
Students submit notes from reading assignment, "Designing Surveys & Questionairres". Here's the sections you DO NOT have to read.
"Pre-Notification Letters", "Notification of Cut-off Date", "Reply Envelopes and Postage", "The Outgoing Envelope and Postage", "The Meaning of Significance"
Project #2 Sampling Survey Project
READING: Here's the link for the reading assignment that presented an overview of how to complete an observational study.
DESIGNING YOUR STUDY/PROPOSAL: Now it's time to pick a theme, form groups, and write a proposal where you document the design of your sampling survey. Topics are listed below.
* School Nutrition: This sampling survey will focus on student preferences regarding future healthy cafeteria offerrings. Leaders will interact directly with Mrs. Hunsaker, the administrator in charge of the cafeteria. Here's a link to the school's Nutrition Services web site.
* Senior Survey: This sampling survey will serve as a preliminary investigation for a census that will be conducted of all graduating seniors in April. Leaders will interact with counseling office administrators that have a stake in these findings. Focus here will be on the college application and selection process. Here's a link to last year's Senior Survey.
* Student Philanthropy: This sampling survey will examine the generosity of GHCHS students.
Volunteer Rates By State (Thanks Majde)
Volunteering in US (2007-2011) (Thanks Peter)
More Volunteer Data By State (Thanks John)
Volunteer Data For 1990-2, 1994, 2000 (Thanks Matt)
Social Insurance & Human Services: (Thanks Michelle)
* Upperclassmen Physical Conditioning: Do students get in better or worse physical condition as they get older? This group will examine random samples of upperclassmen to determine if the they are in better overall condition than the norms observed in the April 2012 Fitnessgram tests of underclassmen.
* Movie Preferences: This sampling survey will examine the movie viewing preferences of high school students. This work will provide background information that will be a shared with film production teams in Mr. Crossley's classes.
DESIGNING YOUR SAMPLING SURVEY & WRITING THE PROPOSAL:
Write four narrowly focused questions that fit within your theme. Two must involve quantitative variables, and two must involve categorical variables. Mr. Nelson will meet with the leaders to discuss the group's proposed questions.
Once Mr. Nelson has approved your questions, students will begin preparing FOUR DOCUMENTS (the proposal, survey questionnaire, response sheet, and promotional flyer).
Leaders will assign roles to each student. BEFORE starting their tasks, students should review the relevant Survey Design Tutorial, and check out some survey documents from previous studies. The template below will guide the groups through the many decisions required to conduct a sampling survey that lacks bias, and maintains the three Inference Conditions (Random Sample, Normal Sampling Distribution, and Independence).
SAMPLING SURVEY PROPOSAL TEMPLATE
DRAFT PROPOSAL EXAMPLE (TEXT ONLY)
IMPLEMENTING YOUR SAMPLING SURVEY:
All students will implement the sampling survey. Teams of two usually work best, but this decision will be up to the leaders and the group at large. Once the data has been collected, the teams will input the data into Excel.
ANALYZING THE DATA & PREPARING A REPORT
All team members will participate in writing the report. Each member will provide one of the following: four-step inference test of significance; a display showing a graphic representation of the sampling distribution and P-value; OR a confidence interval estimating a mean or proportion. Leaders will receive further instructions on the layout of the report, and will be shown examples to follow.
FINAL EVALUATION: Project grading will be similar to the first semester data analysis, excecutive summary reports. The links below provide the leader evaluation forms that will be used in this project.
Leader Evaluation Forms For Mini-Survey Project
INFERENCE MATERIALS
INTRODUCTION TO TESTS OF SIGNIFICANCE: Here's the two tests of significance that we went over in class. The first link is a word file with the questions. The second link is the Excel file that we went over in class.
Introductory Questions, One Mean Test & One Proportion Test
Test of Significance Mean & Proportion One Sample EXCEL File
As requested, I've created PDFs from the Excel Instructional file. They have been orgaized by mean and proportion.
MEAN FOUR-STEP TEST OF SIGNIFICANCE
PROPORTION FOUR-STEP TEST OF SIGNIFICANCE
PRACTICE PROBLEMS: These problems will serve as practice to prepare for the first Spring Midterm. Two problems will be assigned each night for homework, the first set of two is due on Tuesday 1/29.
A1 & B1 Excel Answer A1 PDF A1 Graph PDF B1 PDF B1 Graph PDF
C1 Excel Answer C1 PDF C1 Graph PDF
C3 Excel Answer C3 PDF
A4 Excel Answer A4 PDF A4 Graph PDF
B4 Excel Answer B4 PDF B4 Graph PDF
C4 Excel Answer C4 PDF C4 Graph PDF
FOUR-STEP INFERENCE PROCEDURE FORMS
Confidence Interval, One Sample Mean
Confidence Interval, One Sample Proportion
Test of Significance, One Sample Mean
Test of Significance, One Sample Proportion
Test of Significance, Two Sample, Difference of Means
Spring Midterm #1 - February 11 & 12
Section #1 FINANCIAL FUNCTIONS
Practice Problems For Spring Midterm #1
(Note: On practice test #1, remember to change #1A. from $25,000 to $15,000)
Practice Problems For Spring Midterm #2
Practice Problems ANSWERS For Tests #1 & #2 EXCEL File
Practice Test #1 ANSWERS PDF File
Practice Test #2 ANSWERS PDF File
Section #2 SYMBOLS & SAMPLING SURVEY VOCABULARY
Symbols Practice Test (Refer To Your Glossary For Answers)
Vocabulary Terms For Sampling Surveys
Section #3 INFERENCE
See "Inference Materials" Above For Practice. Be prepared to do one Test of Significance, Mean or Proportion (One Sample) & one Confidence Interval, Mean or Proportion.