Growing trees faster. The concentration of carbon dioxide (CO2) in the atmospher

Question

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.32

(a)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.

(b)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.

Explanation / Answer

Solution:

a)Assume that the 6 circular areas are given in advance. Number the min any order. Use Table B to select 3 for the treatment. We used line104. The first 4 digitsare:5 2 7 1.We cannot use the 7 because it is more than 6. Therefore, we would treat areas 5, 2 and 1

b) Ift he pairs are not given in advance, divide the 6 are as into 3 pairs so that the elements of each pair are close to each other and therefore of similar fertility. For each pair, we randomly pick one of the two to receive the treatment. Label the two areas in each pair A and B. If the random number from Table B iseven, then apply the treatment to area A. Otherwise, apply the treatment to Area B. Alternatively, we could go along the table looking for either a0 or a1, ignoring the other digits. If we find a0 before a1, then treat area A. Otherwise, treat B.

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