The concentration of carbon dioxide (CO_2) in the atmosphere is increasing rapid

Question

The concentration of carbon dioxide (CO_2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO_2 to fuel photosynthesis, more CO_2 may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO_2 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 CO_2. 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. (a) State the null and alternative hypotheses. (Where mu is the mean difference, treated minus control.) H_o: mu H_a: mu Explain clearly why the investigators used a one-sided alternative. The researchers have reason to believe that CO_2 will decrease growth rate. The researchers have reason to believe that CO_2 will increase growth rate. The researchers have no preconceived idea what extra CO_2 will do to the growth rate. (b) Carry out a test and report your conclusion in simple language. (Use alpha = 0.05. Use 2 decimal place) t = Conclusion There is evidence of a increase in growth rates due to extra CO_2. There is no evidence of a increase in growth rates due to extra CO_2.

Explanation / Answer

(a) Null Hypothesis: = 0

ALternative Hypothesis : > 0

where = mean difference in mean increase in base area for treated minus control for 30 to 40 tress.

(B) The reasearcher used one sided alternative because he belived that CO2 will increase growth rate.

(C) Test Static

This is paired data

sd = sqrt [ ((di - dbar)2 / (n - 1) ] = 0.0302

dbar= 1.064

test static

t = dbar/(sd/n) = 1.064/ (0.0302/3) = 61.02

so There is very strong evidence of a increase in growth rate due to extra CO2 .

Pair Control Treated d d^2 1 9.716 10.808 1.092 1.192464 2 7.152 8.22 1.068 1.140624 3 5.616 6.648 1.032 1.065024 Average 7.494667 8.558667 1.064 Std. dev 0.030199

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