In a factory items are produced on three production lines, A, B, and C. At the end of each line the items are packed into boxes of 20. These boxes are then stored in the warehouse. The boxes from each production line are stored in separate stacks. Each stack consists of a 5 × 5 square layer of boxes (i.e. 25 boxes in each layer). As the boxes are filled during the day the stacks are filled in time order, i.e. the items produced earliest are at the bottom of each stack.
A Trading Standards Officer visits the factory and wishes to select a sample of 60 items for testing from the three stacks. The stacks at that time contain 40 layers in Stack A, 10 layers in Stack B and 20 layers in Stack C.
Describe how you would go about choosing this sample using the following methods:
i) Simple random sampling
ii) Stratified sampling and
iii) Systematic sampling
Comment on the advantages/disadvantages of each method.