Carbon dioxide [Chapter 20]. Because plants use CO2 to fuel photosynthesis, more CO2 may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO2 to a 30-meter circle of forest. They selected two nearby circles in each of three parts of a pine forest and randomly chose one of each pair to receive extra CO2. The response variable is the mean increase in base area in m? for 30 to 40 trees in a circle during a growing season. We measure this in percent increase per year. The following are one year's data. This is a matched pairs design. Compute and report differences to +0.001 in the single column table at the lower right. Use a = 5%. Diff (Trt - Con) Pair Control plot Treated plot 9.752 7.263 5.742 10.587 2 3 9.244 8.675
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
STATE:
PLAN:?diff ≡
H0:
Ha:
Method used:
SOLVE: Check all conditions. Show all graphs/formulas used, with the correct values filled in. Report estimate to ±0.001 m2. Report p-value to ±0.0001.
CONCLUDE:
a) Why should one be cautious about reporting the test results from this study?
![Carbon dioxide [Chapter 20]. Because plants use CO2 to fuel photosynthesis, more CO2 may cause trees and other
plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO2 to a 30-meter circle of forest.
They selected two nearby circles in each of three parts of a pine forest and randomly chose one of each pair to
receive extra CO2. The response variable is the mean increase in base area in m? for 30 to 40 trees in a circle
during a growing season. We measure this in percent increase per year. The following are one year's data. This
is a matched pairs design. Compute and report differences to +0.001 in the single column table at the lower right.
Use a = 5%.
Diff (Trt - Con)
Pair Control plot Treated plot
9.752
7.263
5.742
10.587
2
3
9.244
8.675](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d0b94bd-30a2-4551-90fa-e539ece224ed%2F44d91e33-3704-4a63-bb34-27b74f05b02f%2Fu48kpuh.png&w=3840&q=75)
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