The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidl
ID: 3363360 • Letter: T
Question
The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. 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 for 30 to 40 trees in a circle during a growing season. We measure this in percent increase per year. Here are one year’s data:
trees=read.csv("trees.csv",header=TRUE)
trees$Diff=trees$Ctrl-trees$Treat
trees
## Ctrl Treat Diff
## 1 9.752 10.587 -0.835
## 2 7.263 9.244 -1.981
## 3 5.742 8.675 -2.933
sapply(trees,mean)
## Ctrl Treat Diff
## 7.585667 9.502000 -1.916333
sapply(trees,sd)
## Ctrl Treat Diff
## 2.0243790 0.9817632 1.0504939
(a) State the null and alternative hypotheses. Explain clearly why the investigators used a one-sided alternative.
(b) Carry out a test and report your conclusion in simple language (In terms of the question).
(c) The investigators used the test you just carried out. Any use of the t procedures with samples this size is risky. Why?
Explanation / Answer
ans=
a) H0: = 0 vs. Ha: > 0
The scientists state that they expect "greater" growth due to the CO2
b) More CO2 doesn't cause trees to grow faster (P > 0.05).
A "two mean" test uses some complex formulas. Most students will simply enter the data into their TI-83 or 84 (like I did) and use the 2-SampleT-Test
P = 0.12 which is greater than 0.05
Do NOT reject the null hypothesis. The data does not support a difference in growth rates.
c)False. The t-distribution is symmetric regardless of the size of the sample.
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