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Math 114 Projects
PROJECT I: Health and Mathematics
Purpose: To understand how mathematics can be used to decide if a particular health change had a positive effect.
Description: Some say “when will I ever use this math in my real life?” This is my attempt to show you that you can use math as an objective measure in something that can make a difference in your real life. Additionally, many of you who will take statitiscs after this course will have this brief encounter with the topic of hypothesis testing .You will need to calculate a final number but also take into account what the value means in the midst of real life factors that may have skewed your values.
You will colloborate with 4 to 5 other algebra students to decide if a pre-selected health change has made a positive difference. First, you will go to a website that asks you to answer questions regarding your schedule, the type of health change you are most intereseted in committing to for one week and the role you would like to play in the group. Once everyone has answered the questionnaire, we will group you with other students that want to make the same type of change, can hopefully meet when you can, and want to take on different project tasks. We also included some characteristics that we found might produce good group interaction.
Once the groups are formed, the coordinator will send out a message introducing themself and setting up the first meeting. This meeting can be in person or on-line using the mathzone student lounge (see tab called on-line tutor in mathzone). In the first meeting each of you should:
1. Introduce yourselves, perhaps why are you taking this class and state or decide your roles. You may use the roles in the questionnaire or negotiate new roles.
2. Clarify exactly what type of health change will happen in the week and make sure everyone agrees upon the same change. Make sure to clear up ambiguities, for instance if you all decide to walk for an extra 30 minutes/week, do you think the time of day matters? Some possible health changes are listed at the end of this doc.
3. Select a measure of success. For instance, if you decide to measure how awake you feel you will need to assign numbers 0-5 and describe those numbers. You may decide to measure productivity at work somehow. Determining a good measure is difficult. Please decide on something so that you can continue the project. Possible measures are included at the bottom of this doc.
4. Each person in your group will need to give a value of the measure in (3) before the health change begins and then again after they have completed the week. For instance, someone might say that at the beginning of the week (before the health change) that their focus at work was at a 2 (5 being the highest). After the week of additional exercise their focus was at 4. Each person in your group will need to report a number before and after the health change.
5. Your group will need to calculate what is called a test statistic. Here are your steps:
a) For each person calculate the difference between their measure after the health change and before. This should be a nonnegative number. If most of your values are negative please talk to me before proceeding.
b) Given this list of 5 or 6 numbers find the average value. That is, find the average difference.
c) Next you will find what is called the standard deviation. This should be done by hand using the following example. You may also see any introductory statistics book for the formula and other examples.
Example: List of values {2, 4, 1, 2, 1}
Calculate the average = (2+4+1+2+1)/ 5 = 2
Next you will calculate what is called the variance: [ (2-2)^2 + (4-2)^2 + (1-2)^2 + (2-2)^2 + (1-2)^2] / 4
That is, you take each of your values in your list, subtract off the mean, square that difference, add them all up and then divide by (the #in the list – 1).
Next, the standard deviation = sqrt(variance).
Finally, your test statistic called a t-score = (average difference)/standard deviation
Based on statistics, if your t-score > 2.13 then your health change made a difference.
If your t-score <= 2.13 then your health change did not make a difference.
Requirements:
1. Write out each role and the name of the person who played that role in your project
2. Concisely describe the health change your group chose. For instance, everyone decided to walk an additional hour per week.
3. What was the numerical measure of success? If you needed to create values write out what they mean.
4. What may have affected your study outside of the health change? For instance, suppose everyone decided to walk 10 more min/day and your group decided to measure weight. Some people may not be able to lose weight in one week no matter what they do. Some people might lose a lot of weight one week because of stress on the job which had nothing to do with the health change. Please give two possible factors that had nothing to do with your health change.
5. What was the value of the statistic.
6. Based on that value and your factors in #4 what is your conclusion? Please write a complete sentence here. For instance: Our study showed that increasing the amount of sleep by 30 min each night improved our focus at work.
7. State two changes you would make to improve your study if you had to do it again.
Possible Health Changes for ONE week
-- stop or decrease the amount of smoking
-- enhance current exercise plan
a) increase aerobic/cardio time
b) increase weight training
-- start an exercise program
a) walking
b) running
c) aerobics/cardio
d) weight training
-- reduce caloric intake
-- increase protein intake
-- reduce carbohydrate intake
-- drink a glass of milk before bedtime
-- increase the amount of sleep
Possible Measurements (Note they must have numeric values or be assigned numeric values) :
-- weight change
-- productivity at work (you will need to decide what this means)
-- more effective studying (possible measurement here might be quiz grade)
Due Date: Beginning of the 2nd Exam
PROJECT II
Description:In this project you will describe and explore how to make your money grow using standard financial formulas from your book. You and your group members should decide on something you want to puchase in the not so far distant future and how much money you currently have for this item. Next, you will investigate three different ways you can make that money amount grow. For instance, a savings account, a CD and a stock. For each of these you can either find the time it takes for you to purchase the item using these three mechanisms or how much money you will have in each account after some fixed amount of time. Time can be in days, months, years ect., it is your choice.
Requirements: Turn in one project for your group. Put your names in the upper right hand corner and make sure papers are stapled if needed. Include the following:
a)State:
1. The initial amount of money
2. The item you wish to purchase and it's cost,
3. Whether you are looking at time to grow the money or the amount after a fixed amount of time.
b) State the formula used
c) Write the values for each of the variables in your formula for the 3 cases,
d)Describe your results:
1. one sentence stating your final values using the formula for each case and,
2. another sentence for a comment about each case. For instance you might state that this CD has the highest rate of return BUT there would be a penalty if you needed to take it out earlier than the stated number of months. You may mention risk if you so choose.
e)State your sources, for instance a CD on-line? Which bank, stock ect...
Grading
This project is worth 25 points
a) 2 points for including all requirements
b) 10 points for neatness and organizing the information clearly
c) 10 points for the attempting to find the best ways to make your money grow
d) 3 points for interesting/creative comments .
Due Date: Beginning of the Final Exam
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