Question

Sampling the forestTo gather data on a $1200$-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of $1410$equally spaced circular plots over a map of the forest. A ground survey visited a sample of $10\%$of the plots.

a. Explain how you would use a random number generator to choose an SRS of $141$plots. Your description should be clear enough for a classmate to carry out your plan.

b. Use your method from part (a) to choose the first $3$plots.

Short answer

a. The random number generator will assist in the selection of an SRS of $141$plots

b. we will choose the first three four-digit numbers from the $141$plots listed above to determine the first three plots of the $1200$-acre pine forest in the United States.

Step-by-step solution

Part (a) Step 1 : Given Information

We have to explain how would use a random number generator to choose an SRS of 141 plots.

Part (a) Step 2 : Simplification

Foresters were interested in using remote sensing to analyse a pine forest instead of collecting measurements on the ground.

To make an SRS using $141$plots, start with $125$and work your way up to $135$, $145$, and so on. Once you reach $1405$, repeat steps $5$through $15$until you reach $125$, resulting in a sample size of $141$.

As a result, this random number generator will assist in the selection of an SRS of $141$plots.

Part (b) Step 1 : Given Information

We have to use your method from part (a) to choose the first three plots.

Part (b) Step 2 : Simplification

The SRS of $141$plots is chosen using a random numbers generator based on the above component (a).

Thus, we will choose the first three four-digit numbers from the $141$plots listed above to determine the first three plots of the $1200$-acre pine forest in the United States. As a result, any three four-digit numbers from the sample of $141$in part (a) above are chosen.

Consider the following plots: $0005$, $0015$, and $0025$, which were picked from a total of $141$plots.