The concentration of carbon dioxide (CO 2 ) in the atmosphere is increasing rapi

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.

(a) State the null and alternative hypotheses. (Where ? is the mean difference, treated minus control.)

Explain clearly why the investigators used a one-sided alternative.

A. The researchers have no preconceived idea what extra CO2 will do to the growth rate.

B. The researchers have reason to believe that CO2 will increase growth rate.    

C. The researchers have reason to believe that CO2 will decrease growth rate.

(b) Carry out a test and report your conclusion in simple language. (Use ? = 0.05. Use 2 decimal place)
t =  

Pair Control plot Treated plot 1 9.616 10.612 2 7.116 8.196 3 5.692 6.736

Explanation / Answer

(a) Ho: ? =0

Ha: ?<0

B. The researchers have reason to believe that CO2 will increase growth rate.

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(b)

t= mean difference/(s/vn)

=-1.04/(0.042143/sqrt(3))

=-42.74

The degree of freedom =n-1=3-1=2

It is a left-tailed test.

Given a=0.05, the critical value is t(0.05, df=2) =-2.92 (from student t table)

The rejection reigon is if t<-2.92, we reject Ho.

Since t=-42.74 is less than -2.92, we reject Ho.

So we can conclude that the researchers have reason to believe that CO2 will increase growth rate.

7.474667 mean Control plot 8.514667 mean Treated plot -1.040000 mean difference (Control plot - Treated plot) 0.042143 std. dev. 0.024331 std. error 3 n 2 df

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