Chapter 4.2, Problem 86E

(a)

To determine

To describe the design of a completely randomized experiment using six well-separated $30$ meter circular area in a pine forest and sketch the circles and carry out the randomization your design calls for.

Explanation of Solution

The design of a completely randomized experiment using six well-separated $30$ meter circular area in a pine forest can be conducted as:

Now, we have six well-separated $30$ meter circular areas as-

  

Therefore, three of the areas will be treated while the other three areas will not be treated. Now, see row $105$ from table D as:

  $95592,94007,69971,91481,60779,53791,17297,59335$

Now, if the digits is from $\text{1 to 6}$ then the corresponding area will be treated as:

  $\begin{array}{l}\text{9}\Rightarrow \text{Ignore}\\ \text{5}\Rightarrow \text{Treat area 5}\\ \text{5}\Rightarrow \text{Duplicate}\\ \text{9}\Rightarrow \text{Ignore}\\ 2\Rightarrow \text{Treat area 2}\\ \text{9}\Rightarrow \text{Ignore}\\ 4\Rightarrow \text{Treat area 4}\end{array}$

Thus, area $\text{2,4 and 5}$ will receive the treatment while area $\text{1,3 and 6}$ will not receive the treatment.

(b)

To determine

To describe a matched pair design using three pairs of circles that will reduce the extra variation due to different fertility and sketch the circle and carry out the randomization your design calls for.

Explanation of Solution

Thus, a matched pair design using three pairs of circles that will reduce the extra variation due to different fertility experiment can be conducted as:

As we have six $30$ meter circular areas which are $\text{2 by 2}$ adjacent as:

  

Therefore, three of the areas will be treated while the other three areas will not be treated. Now, see row $105$ from table D as:

  $95592,94007,69971,91481,60779,53791,17297,59335$

Now, if the digits is from $\text{1 to 6}$ then the corresponding area will be treated as:

  $\begin{array}{l}\text{9}\Rightarrow \text{Ignore}\\ \text{5}\Rightarrow \text{Treat area 5}\\ \text{5}\Rightarrow \text{Duplicate}\\ \text{9}\Rightarrow \text{Ignore}\\ 2\Rightarrow \text{Ignore}\\ \text{9}\Rightarrow \text{Ignore}\\ 4\Rightarrow \text{Treat area 4}\\ \text{0}\Rightarrow \text{Ignore}\\ 0\Rightarrow \text{Ignore}\\ 7\Rightarrow \text{Ignore}\\ 6\Rightarrow \text{Treat area 6}\end{array}$

Thus, areas $\text{4,5 and 6}$ will receive treatment while areas $\text{1,2 and 3}$ will not receive treatment.