The concentration of carbon dioxide CO2 in the atmosphere is

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 =  

Solution

(a) H_o: ? =0

H_a: ?<0

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

-------------------------------------------------------------------------------------------------------------

(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.