Problem: Growing trees faster. The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because green plants use CO2 to fuel photosynthesis, more CO2 may cause trees to grow faster. An elaborate apparatus allows researchers to pipe extra CO2 to a 30-meter circle of forest. We want to compare the growth in base area of trees in treated and untreated areas to see if extra CO2 does in fact increase growth. We can afford to treat three circular areas.
Required:
(i) Describe the design of a completely randomized experiment using six well-separated 30-meter circular areas in a pine forest. Sketch the circles and carry out the randomization your design calls for.
(ii) Areas within the forest may differ in soil fertility. Describe a matched pairs design using three pairs of circles that will reduce the extra variation due to different fertility. Sketch the circles and carry out the randomization your design calls for.