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Ray Atkinson
Ray Atkinson, Bachelor's Degree
Category: Math Homework
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Experience:  Grad student. Years and years of tutoring. Education, accounting, and math degrees.
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need help with a math project due today at midnight... its

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need help with a math project due today at midnight... its about life expectancy and interpreting models of linear equations and graphs and answering a couple of questions along with complete show of work.... anyone up for helping me?
Submitted: 10 months ago.
Category: Math Homework
Expert:  Ray Atkinson replied 10 months ago.

Ray Atkinson :

Please give details and I will see if I can help.

Customer:

MAT 171 Project I Life Expectancy Fall 2013


Over the last one hundred years, the average life expectancy of both men and women has increased significantly. In this project, you will investigate the trends concerning average life expectancy and use linear modeling to answer questions about these trends.


The purpose of this project is for you to apply concepts we have discussed in class, such as modeling with the TI-83/84 calculator, drawing scatter plots, making predictions, and solving systems of linear equations. Follow the directions for each part. When answering a question you must answer in complete sentences. You may work with a friend, but each person must turn in their own project.


Part I. Visualizing the data


You will need to draw a scatter plot according to the directions below. Use a whole sheet of graph paper. The table below shows the life expectancy at birth, by gender, for the years indicated, beginning in 1900 and continuing through 2000.


Year Life expectancy of males Life expectancy of females


1900 47.9 1910 49.9 1920 55.5 1930 57.5 1940 61.6 1950 65.5 1960 66.8 1970 67.0 1980 70.1 1990 71.8 2000 74.1


Follow the directions carefully.


50.7 53.2 57.4 60.9 65.9 71.0 73.2 74.6 77.6 78.8 79.5


1. Use the horizontal x-axis to represent the year. Label the axis counting by 10s, starting with 1840 and continue through 2020. The origin is still the origin. Indicate on the axis that you are skipping many years


2. Use the vertical y-axis to represent life expectancy. Label the axis counting by 5s. (This means the numbers can increase by 5, this does not mean each horizontal line is an increment of 5. You could use two lines.)


3. Use a plus “+ “ sign to represent the data for men, and plot the points on the graph paper using the year as the x coordinate and the life expectancy of men as the y coordinate. On the same graph, use an “o” to represent the data for women, and plot the points on the graph using the year as the x coordinate and the life expectancy of women as the y coordinate.


Part II. Finding the Linear Models


1. Using the years as x and the life expectancy of males as y, enter the data in your calculator in L1 and L2, respectively. Enter the life expectancy of females as a third list in L3.


2. Set up the Plots options:  Pressing 2nd Y= puts you in the STAT PLOTS menu. Turn on Plot1


and make sure that the Xlist is L1 and the Ylist is L2. Change the


Mark: to the „+‟ (at the bottom of the screen).  You can access the Plot2 menu from the screen you are currently at


by going to the top of the screen and highlight Plot2 then press ENTER. Turn on Plot 2. Change the Ylist to L3. Move the cursor just to the right of the Ylist:. Press 2nd 3 and you should get L3. Make sure the Mark: is the □.


 Use Zoom 9 to view the scatter plot after you have set up the plots.  Change the WINDOW options to match the parameters of your


hand-drawn graph. Now, the calculator‟s graph should resemble the one you drew in part I.


3. Using the CALC option under STATS menu, use LinReg to find a linear model (equation) for L1 and L2. This is the equation predicting the life expectancy for males. Record this equation. Round off the values for a and b to two decimal places.


4. Now find the linear equation predicting the life expectancy for females. This time you need to use L1 and L3 when calculating LinReg. Record this equation. Again, round off the values for a and b to two decimal places.


5. Draw the lines representing the equations you found for the Life Expectancy of Males and the line for Life Expectancy of Females on the graph you created in Part I. To do this -- to pick two values for x that are a multiple of 10 between 1840 and 2000. Then solve for y for each. You will now have two points to help you draw a line. [Write out all the calculations] Do the lines appear to intersect? Where? Give approximate coordinates, based on your graph, as integers. Mark the point on your graph. [These questions need to be answered in complete sentences.]


III. Interpreting the Models


For this section, you need to respond in complete sentences. Make sure you answer the questions thoughtfully and completely. If you are asked to calculate anything, you MUST show ALL of the necessary steps.


1. AccordingtothelinearmodelsyoufoundinPartII,wasthereinthepastor will there be in the future a year in which the life expectancy of males and the life expectancy of females was or will be the same? To answer this question, you must find the point of intersection for your two equations.


You will be solving a system of simultaneous equation. How does your answer compare to the point you found in Part II, #5 above?


2. Useyourmodelstopredictthelifeexpectancyofmalesandfemalesbornin 2015 and in 2025.


3. What do your linear models suggest the life expectancy of males and females to have been in 1850? According to an official source [the writer of this assignment –not me- did not provide this important piece of information], the estimated life expectancy of males born in 1850 was 38 and the estimated life expectancy of females born in 1850 was 40. How do your values compare to these numbers?


4. What are the values for the y-intercepts for both linear models? (Show the work)


Interpret the meaning of these y-intercepts.


5. Analyze the linear models you found in this assignment. Do you think these linear models are valid? Do they accurately describe how long an average male or female lived in the past or will live? Why? Are these models useful? When would one need to use a prediction of life expectancy? This part must be answered in the form of a short essay (at least 1⁄2 a page). State your position and provide arguments supporting your position. You may use mathematically based arguments or other knowledge (facts, not opinions) to make your arguments.

Customer:

I need help on the question number 5 on part 2 and all of the questions on part 3... not that much i think... I needed for tonight at midnight... you think you can do it? i need all work shown as well thanks...

Customer:

hey you think you can help me?

Ray Atkinson :

Correct me if I am wrong. You just need the linear regression equation and evaluate them at 1850, 2015, and 2025?

Customer:

idk i just need the answers for the question 5 from part 2 and the rest of the answers for the questions on part 3 from 1-5

Ray Atkinson :

Are the values given next to the years the males and a line below that the females?

Customer:

yes

Customer:

how do you attache documents in here

Ray Atkinson :

Ok, last question. what time is it where you are?

Customer:

so i can attache the project

Customer:

the time is 9:44

Ray Atkinson :

Excellent. 2:16 to go.

Customer:

yes

Customer:

u think u can help me in the 2:16?

Ray Atkinson :

If you do not have a paper clip icon above where you type, you can use sendspace.com to upload the file and give me the link for the download

Ray Atkinson :

unless I have technical problems, I can get it done in plenty of time.

Customer:

how do i send it to you on there?

Ray Atkinson :

If you upload the file there, there is a button that says "copy link." Click that, come back here, and paste.

Customer:

http://www.sendspace.com/file/z7mr8k

Customer:

i attached the project... i have already done the 1 part of the project... and part 2 except for question number 5 and i also need part 3 ...

Customer:

where you able to get the project to work correctly?

Ray Atkinson :

I am working on the regression right now.

Customer:

can you show the work?

Customer:

and answer the questions in the order they go thanks

Customer:

???

Ray Atkinson :

working on it right now.

Customer:

thanks

Customer:

when you get questions done could you send some to me so i can copy them down to a piece of paper or are you gonna send them all at once?

Ray Atkinson :

Question for you. Can I do the work in Excel, or does it have to be done by hand?

Customer:

it has to be done by hand... the work has to be shown on paper step by step... its only for the 6 questions

Ray Atkinson :

Ok got it.

Customer:

i can graph the graph required on question 5 if i have the answers

Customer:

question... are you doing all of it or just the ones i asked?

Ray Atkinson :

Sweet. I can use a calculator to get the lines. Let me get them so you can get the graphs done.

Customer:

yeah thanks

Ray Atkinson :

So you need 2.4, 2.5, and all of 3

Ray Atkinson :

!! The instructions say to use a calculator !!

Customer:

to be sure 2.3 2.4 2.5 and all of 3

Customer:

yup i know

Ray Atkinson :

did your instructor tell you different rules?

Customer:

calculator is fine but the other questions say (show wall of work and calculations)

Customer:

so please just show the work and answer the questions like the project asks... in full sentences and with all calculations and all work... thank you very much! :) i appreciate it

Ray Atkinson :

You can get started on this
Equation for males is y=0.26x-445.55
Equation for females is y=0.31x-538.21

Ray Atkinson :

that is actually the answers for 2.3 and 2.4

Customer:

got those thanks

Customer:

i will wait on the rest

Customer:

:)

Ray Atkinson :

Using 1900 and 2000 as the points to draw the regression lines:
0.26(1900)-445.55 = 494-445.55 = 48.45, so (1900, 48.45)
0.26(2000)-445.55 = 520-445.55 = 74.45, so (2000, 74.45)

0.31(1900)-538.21 = 589 - 538.21 = 52.79, so (1900, 52.79)
0.31(2000)-538.21 = 620 - 538.21 = 81.79, so (2000, 81.79)

Ray Atkinson :

That is 2.5

Customer:

whats 2.5 for?

Customer:

got it thanks

Ray Atkinson :

(any two lines with different slopes are going to cross)
It looks like they cross about the year 1850 with a value around 35 years

Ray Atkinson :

Write this:
The lines definitely cross, since they have different slopes. They cross near the year 1850 at a life expectancy of about 35 years.

Ray Atkinson :

Ok, now for part 3 and the calculations.

Ray Atkinson :

y=0.26x-445.55
y=0.31x-538.21

Subtract line 2 from line 1

0 = 0.05x-92.66
92.66 = 0.05x
x=1853.2

0.26(1853.2)-445.55 = 481.832-445.55 = 36.282

the intersection is (1853.2, 36.282)

Ray Atkinson :

those are quite close to my estimate from the graph

Customer:

alright thanks.. im copying them down and checking them as they go ... if i have question i will ask them as i get done copying each one thanks

Ray Atkinson :

Males at 2015 are 0.26(2015)-445.55 = 523.9 - 445.55 = 78.35
Males at 2025 are 0.26(2025)-445.55 = 526.5 - 445.55 = 80.95

Ray Atkinson :

Females at 2015 are 0.31(2015)-538.21 = 624.65 - 538.21 = 86.44
Females at 2025 are 0.31(2025)-538.21 = 627.75 - 538.21 = 89.54

Ray Atkinson :

Males at 1850 were 0.26(1850)-445.55 = 481-445.55 = 35.45
Females at 1850 were 0.31(1850)-538.21 = 573.5-538.21 = 35.29

Ray Atkinson :

The regression lines calculated return estimates for the year 1850 that are slightly under the given facts. Since the difference is less than 5 years, I would still call that reasonably accurate.

Customer:

okay im getting confused... im just now starting on part 3 which answer belong to which question?

Ray Atkinson :

The y-intercept would be the life expectancy for the year 0. Since the estimates would be -445.55 years of age and -538.21, the regression line is meaningless towards that point.

Ray Atkinson :

From the 2 equations and the simultaneous equations to my "quite close" statement is 3.1

Ray Atkinson :

The calculation for 2015 and 2025 are 3.2

Ray Atkinson :

The numbers for 1850 are 3.3

Ray Atkinson :

My comment about year 0 is 3.4

Ray Atkinson :

Now, I need to do some writing for 3.5

Customer:

okay im copying down all of this information ... thanks ... good so far

Ray Atkinson :

I am normally a very concise writer, so I am trying to pad the text out without looking fake. You may (very likely) want to reword what I am writing to be more your style.

Ray Atkinson :

I am a math/accounting major. Not English.

Ray Atkinson :

The linear models are valid, within a limited window of time. Solving for y=0, both equations hit y=0 in the early 1700s, apparently saying that no one lived at all before then. Since this is nonsense, the life expectancy regression line for longer periods must either not be linear, or else the slopes must be shallower. The lines are probably reasonably accurate for the time periods covered. The values for 1850 were close (within 15% off the real values) and modern numbers are done carefully. As for predictions for the future, there is no validity. There could be a medical breakthrough tomorrow that doubles the life expectancy. As for the models usefulness, they do show some interesting information. They definitely show that people are living longer as time goes by. Men’s expectancy goes up 2.6 years every 10, and women’s goes up by 3.1 years every 10. This leads to speculation as to why. Is it nutrition, medicine, crime, environment, evolution? Questions are the beginning of the scientific method, and studies are done all the time in an attempt to explain the facts. Besides all that, life expectancy tables are used every day by life insurance companies as a guess as to how long someone will life to make payments before the company has to pay back.

Customer:

okay sounds good to me

Ray Atkinson :

217 words is almost a half page. The prof should be happy with that

Customer:

yeah i think that is enough... thanks .. all is good...

Ray Atkinson :

If you want to pad that out more, be my guest.

Ray Atkinson :

and fix the typo in the last sentence.

Ray Atkinson :

life -> live

Customer:

yeah thanx

Ray Atkinson :

If there is anything you need clarified, please ask. Please do remember to rate my answer when you are satisfied. If I have given excellent service, consider giving a tip.

Customer:

yes thanks... im still copying everything down.. and yes i will rate your question... thanks for all i appreciate it.

Ray Atkinson :

You are more than welcome. If you need me in the future, you can ask for me by name in the question.

Ray Atkinson, Bachelor's Degree
Category: Math Homework
Satisfied Customers: 1786
Experience: Grad student. Years and years of tutoring. Education, accounting, and math degrees.
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