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:

Pair	Control Plot	Treated Plot	Treated-Control
1	9.752	10.587	0.835
2	7.263	9.244	1.981
3	5.742	8.675	2.933

1. State the null and alternative hypotheses. Explain clearly why the investigators used a one-sided alternative.

2. Carry out a test and report your conclusion in simple language. [Hint: These are matched samples, whereas the previous question was about unmatched samples. Your methodology should differ from question 2. Also, you may use the =t.dist function in Excel rather than Table C in order to get the actual p-value.]

3. The investigators used the test you just carried out. Any use of the t procedures with samples this size is risky. Why?

Answer 1

t-Test: Paired Two Sample for Means
	treated	control
Mean	9.502	7.585666667
Variance	0.963859	4.098110333
Observations	3	3
Pearson Correlation	0.995851579
Hypothesized Mean Difference	0
df	2
t Stat	3.159644096
P(T<=t) one-tail	0.043627955
t Critical one-tail	2.91998558
P(T<=t) two-tail	0.08725591
t Critical two-tail	4.30265273

TS = 3.15964

p-value = 0.04326

p-value < 0.05

hence we reject the null hypothesis

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