Let's say there are N chunks of metal, each are 4 inches thick. They are to be hammered and reduced to following best possible sizes: 1, 2, 3 or 4 inches. If we were to use sampling to get an estimate of possible reduction in the total number of inches in all the N chunks combined, how would we determine the sample size, and the formula for estimation, variance and accuracy?
I am thinking of this like a polling problem, where M/N people are asked to answer a multiple choice question. For eg. each chunk is asked, how many inches can be reduced from you? There are 4 answers. Most of the sampling theory stuff on the web talks about answering yes/no questions. Is there some theory which talks about multiple choice questions?