Welco Lumber Company is based in Shelton, Washington, and is a privately held company that makes cedar siding, cedar lumber, and cedar fencing products for sale and distribution throughout North America. The major cost of production is the cedar logs that are the raw material necessary to make the finished cedar products. Thus, it is very important to the company to get the maximum yield from each log. Of course, the dollar value to be achieved from a log depends initially on the diameter of the log. Each log is 8 feet long when it reaches the mill. The file called Welco contains a random sample of logs of various diameters and the potential value of the finished products that could be developed from the log if it is made into fence boards.
a. Calculate the sample mean potential value for each diameter of logs in the sample.
b. Discuss whether there is a way to determine how much sampling error exists for a given diameter log based on the sample. Can you determine whether the sampling error will be positive or negative? Discuss.