MDM4U Culminating Project

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Eileen Golden
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1 MDM4U Culminating Project The culminating project is a statistics project requiring the collection, organization, analysis and presentation of information related to a hypothesis investigated by the student. The project involves a written paper, an Excel spreadsheet and an in-class presentation in front of your peers. Maximum 2 people per project. The required sample size is 50 responses to your survey. Requirements for the final paper: 1. Title page 2. Table of Contents referring to sections and page numbers 3. Summary 4. Research Questions and Hypothesis 5. Description of the Data Collection Process 6. Individual Question Analysis for each question included in your survey 7. Research Question Analysis 8. Conclusion 9. Appendices Title Page The title page should include the name of your project, the date, the names of group members and the name of your teacher. Summary In one page, summarize your entire report. A summary section is something that would be read by a manager who didn t have enough time to read the entire report, so make sure that you have enough details that it can stand by itself. At the very least, include the following: - Problem: a clear statement of what you were trying to learn - Plan: the procedure that you used to carry out the study (how did you choose people? How did you measure? Who did the measuring? What methods did you use?) - Data: the date are collected according to the plan (what data did you collect? Note any departures from your plan) - Analysis: The data are summarized and analyzed to answer the questions posed (numerical, graphical, informative sentences) - Conclusions are drawn about what has been learned (note any biases, suggest further studies)

2 Problem Draw a Mind Map that leads to your thesis statement. It should be quite detailed and have many levels. Main thesis question. The main thesis question is the theme of your report (e.g. why do teenagers pay so much for car insurance?) Problems: the sub-questions that you will use to solve your main thesis question. These should be specific enough that they contain the variables that you will measure. The problems may evolve slightly throughout the life of your project. (What is the relationship of death rates for various age groups? What is the relationship between insurance rates and age? What are the probability distributions of collisions with age (by gender) and with drivers killed (by gender) with respect to age? What effect does sample size have on the accuracy levels of the above results? Does the distribution of males follow a normal distribution?) Define the population, population characteristics (% gener, mean rate of death for various age groups, mean rate of collision for various age groups), independent variables (age, gender), dependent variables (insurance rates) and other variables as required by your topic. Draw a Cause and Effect diagram (AKA fishbone diagram see sample projects) to find other variables that could affect the outcome of your measurement. Make sure that you deal effectively with many of the variables that come up on your fishbone diagram. Survey Design / Data Gathering Process The survey is the primary means by which you are collecting data for your project. The survey should consist of at least 5 questions per person involved in the project. However, do not approach the creation of the survey as getting enough questions each question should only be included in your survey if there is a particular purpose. Questions that collect demographic information (age, program of study, gender, etc) are not considered to be part of the 5 questions per person but should be included in the survey. Your survey should include an introduction and a statement of purpose in addition to a notice about confidentiality. If you have an idea involving the collection of data that comes from sources other than a survey (e.g. a reputable online database), this is possible ask first. In this section, it is expected that you describe how you or the group went about collecting responses to your survey. Include the intended population from which the sample was drawn from and how the sample was selected (referring to specific sampling techniques). Indicate any problems with sampling here included rejected surveys. If your data was found online, then it is your job to find out as much as possible about how the data was obtained. That information should be included here.

3 Individual Question Analysis For each question in your survey including the demographic information, it is expected that one graph is produced, with a minimum of 3 different kinds of graphs (histogram, box plot, pie chart). There must be at least ONE histogram as it is included in the rubric. Describe the features of each graph you create. For each question, indicate the variable type (categorical, discrete, continuous) and what measures of central tendency are available. Calculate those measures of central tendency. These calculations should be completed in the Excel spreadsheet, and included in tabular form in the written project. Also include, when possible (if the data is numerical), the 5 number summary and standard deviation. For numerical data, identify whether any outliers are present in the data and include a method for addressing the problem. Two Variable Analysis (Research Question Analysis) The analysis you use depends on the type of variables you are relating in each research question. Two numerical variables One numerical, one categorical Two categorical Linear regression Comparison of means Chi-squared Two numerical variables You must create a scatterplot and fit a least squares regression line to the data. On the scatterplot, show the equation of the linear model and the coefficient of determination. Calculate the correlation coefficient and the least squares regression line. Explain the meaning of the coefficient of determination and explain whether the correlation coefficient is significant considering the sample size. One numerical variable and one categorical variable One numerical, one categorical Calculate the mean for each group defined by your categorical variable. Do a comparison of means test and include the interpretation of the test. Also, create a box plot for each group and graph them together on the same axis for comparison purposes. Describe the differences between the two box plots mentioning the differences in range, median, and interquartile range. Two categorical variables Organize the count for each variable in a contingency table which may be 2x2 or larger. Include the totals in the right and bottom margins.

4 Refer to our notes from earlier in the semester on how to write a statement about the relationship between two categorical variables. Conclusion In the conclusion, summarize the findings for each research question and refer back to your research questions. Decide whether to reject or fail to reject the hypothesis that you made earlier. If your data was collected from a sample that was not properly random be honest your conclusion should include statements that reflect this. Any limitations should be stated. Outline in detail where the project could go if it was analyzed further. Appendices Your appendices includes your Excel file which shows the data that you gathered, calculations that were done and a glossary of terms. Presentation You will have a maximum of 15 minutes to present your project (time it when practicing) Pick out the most important parts of your written report and explain them to the class You may wish to add interest to your presentation by using PowerPoint and demonstrations. The class will have a few minutes after your presentation to ask you questions about your report. About 5 of your classmates will be randomly selected to do an evaluation on your presentation. I will take their comments into consideration when calculating your mark. Formatting Instructions for Reports 1. Do not use more than two different fonts. 2. Use a sans-serif font for the titles (e.g. Arial, Arial Black, comic sans MS) and serif for the text (e.g. Times New Roman, Helvetica). It helps with readability. 3. Avoid underlining. It makes words harder to read. Use bold or italics. 4. Use paragraphs. Use the spell check. 5. Avoid full justification of the text. It looks weird especially when the line is not full. 6. Use white space put space around the different sections of text. It helps with readability. 7. Source anything that didn t come out of your own head.

5 Due Dates PROJECT PROPOSAL Tuesday May 31 Includes mind map and fishbone diagram DATA GATHERING PLAN Wednesday June 1 COLLECTED DATA Monday June 6 INDIVIDUAL QUESTION Wednesday June 8 ANALYSIS RESEARCH QUESTIONS Monday June 13 ANALYSIS CONCLUSIONS Tuesday June 14 PRESENTATIONS June 15,16,17 random order determine on June 14 FINAL DUE DATE June 18 Final due date: by June 18 th at the latest. This is to allow some small corrections after presenting your project. No late papers will be accepted (this means a zero for 30% of your total mark) What to send? Your document in Microsoft Word format, your spreadsheet containing calculations, and your Presentation file, zipped together.

430 Statistics and Financial Mathematics for Business

Prescription: 430 Statistics and Financial Mathematics for Business Elective prescription Level 4 Credit 20 Version 2 Aim Students will be able to summarise, analyse, interpret and present data, make predictions