ENVS 202 Take Home Final Exam

Date Due: June 12, 5 pm

How to turn in to the exam. Choose one of the options listed below:

Helpful Hints:

You may and are encouraged to work with up to 3 other persons on this exam for a total group size of 4. This exam is long and dividing up the work will save a lot of time. If your looking for exam partners, post something to the feedback page.

Make sure you read the directions!!! If you don't read the directions you won't do well. Read the directions, even though directions are boring, directions should be read. Read the directions, Show All Work

If you wait until a day before this exam is due, to start it, you will likely not do well. In the past, some students have gotten 100% on this exam, while others have gotten 35%. Start doing this exam early. You have a week to get it done. Use it. Access the statistical graphical tool on Campus. If you rely on busy modem lines during finals week you are only making life difficult for yourself. Read the directions, Show All Work.

The total points available on the questions are 410 . The point totals for each question are summarized below as a guide to help you:

 1. 15 pts  7. 15 pts  13. 15 pts 19. 15 pts
 2. 25 pts  8. 10 pts  14. 10 pts 20. 30 pts
 3. 20 pts  9. 35 pts  15. 10 pts 21. 10 pts 
 4. 10 pts 10. 15 pts  16. 20 pts 22. 15 pts 
 5. 15 pts 11. 15 pts  17. 20 pts 23. 20 pts
 6. 15 pts 12. 20 pts  18. 15 pts 24. 20 pts

In addition, there are also 40 points available for overall presentation of your exam. Sloppy and poorly organized exams will receive less of these presentation points than well organized exam. Remember part of process here is to write up a good report! So the final point total is 450

This exam has a logical flow to it. Answers and results from one set of questions will be used later. Hence, as in real life, its possible that an error can propagate throughout the exam and affect your later derivations and conclusions so take your time and be careful.

Read the directions, even though directions are boring, directions should be read. Read the directions, Show All Work





Now, on to the Exam

Congratulations, you have just started your first day on your new job at Paper, Incorporated: Sustainable Wood Products (hereafter PISWP). The goal of PISWP is to not only have an acronym which is hard to pronounce while retaining saliva at the same time, but also to dominate the paper products market. Your job is in the area of technical reporting and resource management. That is, the future of PISWP depends entirely on your ability to understand data, manage a project and to make sensible decisions.

PISWP upper management feels that it now has a competitive advantage in the market place due to a secret kind of fast growing tree (known as the Growth-O-Rama tree) that they have developed. This tree requires a fair bit of light (sunshine) coupled with occasional precipitation as well as augmentation of soil nutrients using some specialized fertilizer (RED GULP #47 or BLUE GOO #33) that PISWP has also developed.

PISWP is planning to seed its land with the Growth-O-Rama tree. The land owned by PISWP is 100,000 acres in the watershed of the wild Snognurtle river. The Snognurtle is one of the main migratory channels of the Single-Eared Toothless Orange Ratfish ( SETOR ). and the Snognurtle watershed is the native habitat of the rare, but not yet declared endangered, flying yellowrat teeter-toad (the FYTT). On very rare occasions, particularly hungry SETOR have been known to leap out of the Snognurtle and snatch an FYTT in midflight. However, no one has actually observed this event.

The source of the Snognurtle lies in the heavy snowpack of the Ill Gotten Gains mountainous area. There are 4 major tributaries which combine to make the mighty Snognurtle. In order of increasing upstream distance, these tributaries are 1) Pulltab brook, 2) Sixpack stream, 3) Clueless creek and 4) Bottlecap river. Shortly after Clueless Creek meets it, the Snognurtle goes around Progress Bend where it is surrounded on both sides by an extensive flood plain known as Wasted Flats.

It is your job to make sure that PISWP makes a profit while attempting to maintain compliance with any EPA regulations as well as to preserve the nature of the Snognurtle watershed. Despite any moral obligations that you might have, you still need a job and this is it.

Your technical report and projection management will consist of many steps. These should be followed and presented in logical order. You will need to make use of the classroom statistical tools and you will certainly have to show (graph) all relevant data. Make sure you pay attention to the possibility of deviant data which should be rejected.

Within the narrative below, individual questions are coded in boldface. Make sure that you show your work including any graphs that you make. Document your case!








Your first task is to determine the potential growth of the Growth-O-Rama tree on Wasted Flats. The laboratory tests done at PISWP yield the following data.

Column 1= precipitation in units of inches per year
Column 2 = growth rate of tree diameter in units of inches per year

Precip     Growth rate  

   5          0.25     
  10          1.3
  15          2.0
  20          3.8
  25          5.2
  30          6.4
  35          8.3
  40          7.2
  45         10.5
  50         11.0
  55         12.6
  60         14.2
  65         16.0
  70         16.6
  80         17.1

The Wasted Flats official rain gauge has recorded these amounts of annual rain for the last 36 years (data values in inches per year):

18.83 19.78 20.26 21.81 24.50 25.66 26.29 28.63 29.80 31.91 32.60 32.74 32.75 33.44 35.09 36.28 36.34 36.77 50.63 40.30 40.47 40.90 41.55 41.78 42.56 43.30 45.02 45.67 49.01 50.41 53.27 38.51 17.42 21.85 48.79 37.53

1. What is the mean annual rainfall and the dispersion? What is the probabilty that in any given year it will rain more than 45 inches?

2. Plot the lab data to determine if there is a correlation between growth rate and annual precipitation? If so, what is the best fitting relation? Are there any individual data points which deviate by more than 2 dispersion units from the mean relation? If so, does their removal significantly lower the scatter in the relation?

In another report titled Effects of PISWP In House Fertilizers on Growth-O-Rama growth rate you see this data

Column 1 = concentration of RED GULP# 47 or BLUE GOO #33 in parts per million
Column 2 =  increased growth rate of tree diameter in units of inches per year
that results when you add  RED GULP# 47 or BLUE GOO #33 to the soil

RED GULP# 47    Augmented growth rate   BLUE GOO #33 Augmented growth rate

     1               0.05                  1             0.7
     2               0.3                   2             1.2
     3               0.7                   3             1.3
     4               0.75                  4             1.8
     5               0.95                  5             2.4
     8               1.40                  8             3.5
    10               2.20                 10             3.8
    20               4.10                 20             4.4
    40               7.80                 40             4.8



3. If PISWP want to produce an augmented growth rate of 10 inches per year how much RED GULP #47 should be used? How much BLUE GOO #33 should be used. Which of these two estimates is the most reliable and why?

A harvestable Growth-O-Rama is one which has a diameter of 75 inches.

4. Assume that you add no fertilizer to the soil so that the growth rate is determined only by the precipitation. If you planted in Wasted Flats today, what would be the expected time (in years) it would take to produce the first harvest?

5. Over this time period, what would the average annual rainfall have to be in order to produce an average tree diameter of 120 inches?

6. Using a fertilizer content of 15 parts per million of RED GULP #47 , how much less time would it take for the average tree to reach a harvestable diameter?

Your boss who only cares about the bottom line looks at your data and decides that its possible to develop a new product line of multicolored Post-It notes specifically designed for computer monitors, based on harvesting trees of only 15 inches in diameter. However, your boss is initially opposed to the use of fertilizer but nonetheless desires to produce a harvestable crop of 15 inch trees every year.

7. How much rainfall is required to produce a 15 inch tree in one year and what is the probability of this happening? If the climate suddenly changes so that the annual rainfall is only 25 inches, how much BLUE GOO #33 do you need to add to the soil to grow a 15 inch diameter tree in 1 year.?


While pondering one day about how to best please your boss you were walking around PISWP aimlessly one day and you fell in a hole. At the bottom of the hole was a sign that read:

" PISWP Archive Section; Proceed at your own risk!"

So you decide to rummage through the archives and you notice and old, worn-out report with the title

Field Tests of Growth-O-Rama: Initial Planting

Knowing that your lab conditions can't exactly duplicate the real conditions, you seize upon this opportunity to study this field data. You discover that somebody actually went out and planted 1000 seedlings in the Pulltab Brook, Sixpack Stream, and BottleCap river areas, sometime within the last 10 years, however, its not clear from the report exactly when each planting occurred. Clearly this data is an important supplement to your lab data.

8. Explain what you would do in order to determine the distribution of tree diameters in these areas without actually measuring 1000 trees.

Assuming you have followed your method outlined above, you have measured the following tree diameter in the three areas: (all data in inches) (Remember, always look at your data; don;t just turn the crank)

Pulltab Brook: 42 42 41 43 44 40 42 41 45 39 40 44 42 39 38 42 41 42 52 54 54 55 55 53 54 57 52 65 66 67 64 68 67 78 79 82 86 44 42 44 48 46 41 70 98 38 55 54 53 65 66 64 68

Sixpack Stream: 56 69 72 77 79 56 62 53 51 61 52 69 72 68 66 63 62 65 61 66 72 72 59 73 65 76 67 51 70 63 59 65 64 62 73 67 71 74 82 81 80 76 74 78 78 82 85

BottleCap River: 54 54 58 64 63 57 55 53 52 61 46 40 44 49 57 65 57 54 59 60 61 57 58 50 54 66 54 53 56 52 63 50 57 58 61 55 57 68 56 55

Eager to further please your boss, you subject this data to the analysis that you learned in ENVS 202 while simultaneously marveling that you actually learned something in college that was useful.

9. For each of the three locations, determine the approximate number of trees that can be harvested right now (e.g those with diameters 75 inches or greater) so that PISWP can get their designer Growth-O-Rama beer coasters into the market. Make sure you assess the reliability of your estimates (that's why this question si worth 30 points).

Upon informing your boss that some harvestable Growth-O-Rama already exists on land she owns, she insists insists that the Company Christmas Card should show the employees standing in an arm circle embracing a Growth-O-Rama with a 90 inch diameter.

10. Which of the three sites has the highest probability of having a Growth-O-Rama tree of diameter 90 inches and why?

11. Determine if there is a significant difference in the mean diameter between the BottleCap River stand of Growth-O-Rama compared to the Sixpack Stream stand

Your boss has just read a story in the magazine TreeHarvester, about the rival company, Trees for Lots of Profit (TFLOP) and its discovery of a small grove of Growth-O-Rama trees that have the same characteristics as the BottleCap River species of Growth-O-Rama. Your boss has read the following in the TFLOP Corporate Report :

TFLOP is the industry leader in developing new wood products. An experimental tree, of TFLOP design, has been growing on TFLOP land for the last seven years. One-third of these trees are already 70 inches in diameter

Your boss panics and starts screaming for you and she shoves the report in your face and screams "We're screwed, look at that, 70-inches - do we have 70-inches?, Well do you!".

You decide that corporate espionage is in order and undertake a stealth mission to go actually inspect the TFLOP stand of Growth-O-Rama. After paying off several of their employees, you discover the location of their test stand. Unfortunately, when you arrive at the stand in the middle of then night you find it heavily guarded. However, you notice that the guards belong to the "Union of Guys that Guard Trees" and you know that union rules require that the guards take a coffee break from 12 to 12:15 am (well at least that's what the Union of Guys that Guard Trees Web page says ...). Timing it right you manage to sneak in and randomly measure the diameter of 9 trees before coffee break is over. You hastily scribble down in your note book the following data:

48 50 62 51 45 49 57 46 63

12. From your data, determine the probability that the statement in the TFLOP corporate report about 70-inches is, in fact, the truth. In addition, to help pacify your boss, show her that there is no significance difference in mean diameter between your BottleCap Growth-O-Rama and those of TFLOP and that, therefore, TFLOP is not ahead of you.

While surveying the terrain map of PISWP land, your boss notices that 25,000 acres are situated on the Wasted Flats flood plain. She formulates a plan of seeding that area with Growth-O-Rama seeds next fall. You remark that Growth-O-Rama seedlings don't do particularly well in floods. Tiring of these complications, your boss makes you prove how big a problem it really is. After surveying Wasted Flats you surmise that each foot the river is above flood stage inundates 2500 acres. The river floods every spring and the flood data indicate the following flood stages for the last 16 years:

Feet above flood stage: 1.5 3.5 4.5 4.8 3.5 3.0 2.0 5.6 7.5 5.5 3.5 5.5 2.5 3.5 4.2 5.0

13. How many acres would you recommend be used for planting assuming that you use a standard of the 100 year flood?

14. What is the probability that all 25,000 acres will be wiped out during one spring flood?

Your boss desires to plant a total of 2 million trees on the Wasted Flats flood plain. Before this is done, some soil analysis is required. You survey the nitrogen content at the four possible planting sites and get the following data:

In addition you measure the density of the Growth-O-Rama stands at PullTab Brook, Sixpack Stream and BottleCap river and they are

In addition, the measured population of the FYTT




15. What should the approximate concentration of nitrogen be in the Wasted Flats flood plain to facilitate the growth of 2 million trees? In doing this calculation make sure you factor in the 100 year flood data from question 13.

The miracle fertilizer RED GULP #47 has 20 times the equivalent power of nitrogen both as a fertilizer and a pollutant in the ecosystem. This means that 1 ppm of RED GULP #47 is equivalent to 20 ppm of nitrogen.

16. In order to reach the yield calculated in question 15, how much of RED GULP #47 has to be added to the soil at Wasted Flats which has a nitrogren concentration of only 40 parts per million? What would be the expected total growth rate of these trees in units of inches of diameter per year?

The EPA has granted a permit to PISWP to plant Growth-O-Rama seeds in the Wasted Flats area. However, the EPA has laid down strict guidelines. All Growth-O-Rama harvesting operations must simultaneously support a FYTT population of at least 8 per acre as that is the minimum FYTT density required for them to procreate.

17. Can you plant two million trees on the Wasted Flats flood plain area near Clueless Creek and still be in compliance with the EPA standard? If so, prove it. If not, why not?


Flooding on the Snognurtle is governed by the runoff into its four tributaries. In order to expand the PISWP profit base, a spinoff company called Environmentally Friendly Wilderness Destruction and Recreation,Inc. (EFWDRI) has been formed. EFWDRI allows land to be cleared along the various tributaries for the purpose of installing recreational wilderness paint-ball arenas to increase tourism in the area. You have set up rain gauges and flow meters on each river to correlate the annual local precipitation with the contribution of each tributary to the spring time flood even. You have only 5 years worth of data which are as follows: (the data are given in X,Y pairs where X represents annual precipitation in the local watershed in units of inches and and Y represents flood stage contribution in units of feet at the Wasted Flats flood plain)

In addition, you have measured how the effects of acreage clearing has increased the runoff. You find that when 200 acres were cleared runoff increased by 40% at BottleCap River, 10% at Pulltab Brook , 5% at Sixpack Stream and 1% at Clueless Creek.

19. Based on this data, in which watershed would you recommend that land be cleared for wilderness paint-ball arenas and why would you make this recommendation?




20. Which area would your strongly recommend against clearing for a paint-ball arena and why?

Since you had done such a good job on this recommendation, you were awarded a vacation. When you returned from your vacation you saw some promotional literature on the new 200 acre paint-ball arena in the Sixpack Stream area, a 300 acre arena at Pulltab Brook, and a 400 acre fully digital arena on the banks of the BottleCap River.

The next year it rains 40 inches in the Sixpack watershed and 48 inches at the other two locations.

21. What is the size of the flood in the spring at Wasted Flats flood plain and what is the contribution from each of the individual tributaries to that flood ?

22. What happened to the Growth-O-Rama stand that was planted on the flood plain.

A congressional hearing results from the Flood and you are called to testify. Your boss tries to claim complete relief from the government by attributing the flood to an act of nature.

23. Although it will cost you your job, you feel obligated to tell the truth. State why this event was not an act of nature and instead why it had a reasonable probability of happening.

As the hearing continues an environmental group contends that the activities of PISWP in the Snognurtle Watershed has seriously decreased the number of SETOR swimming up stream. They offer the following SETOR counts obtained at the SETOR -o-meter downstream from Wasted Flats. The SETOR -o-meter has a random error of 20,000 counts. Here is their data:

  
        Pre-PISWP counts: 75,000 105,000 85,000 165,000 135,000
                             115,000 95,000 65,000 80,000

        Post-PISWP counts:  90,000 50,000 95,000 110,000

24. Does this group have a legitimate claim that SETOR Counts are significantly down? If so, why? If not, why not?

After the hearing you encounter SunShine MoonBeam, current head of the Sierra Club. She accuses you of personally destroying a Wilderness Area based on the business practices of PISWP ? In fact, she plans to put you on the cover of her latest publication "Stupid White Men". In your defense, you hand her a copy of your letter of resignation from PISWP

25. What should be said in that letter to make PISWP accountable for their actions and absolve you of any personal responsibility