Question

Timber! A lumber company wants to estimate the proportion of trees in a large forest that are ready to be cut down. They use an aerial map to divide the forest into $200$equal-sized rectangles. Then they choose a random sample of $20$rectangles and examine every tree that's in one of those rectangles.

a. What is the name for this kind of sampling method?

b. Give a possible reason why the lumber company chose this method.

Short answer

(a) The name of the sampling method is a cluster sample

(b) This method is chosen as it is both cost and time-efficient

Step-by-step solution

Part (a) Step 1: Given information  

We need to find out the name of the method of sampling

Part (a) Step 2: Explanation 

Every tree in the supplied sample is in the sample, which is a random sample of $20$rectangles (as they are examined).

We can see that the rectangles are the subgroups, and that the entire selected rectangle is in the sample (since every tree in the rectangle is in the sample), implying that the sample must be a cluster sample.

Part (b) Step 1: Given information 

We need to find the reason for choosing this method of sampling

Part (b) Step 2: Explanation 

This method was most likely chosen because it is more time and cost-effective than other methods, as finding the equivalent trees using a simple random sampling from the entire area or a rectangle of the area would be quite a time consuming and costly (as there are many trees in an area and trees in a forest are often not placed in straight lines or defined patterns).