Here is the question:
When using stratified sampling, does everyone in the population have an equal chance of being selected?
My initial thought is that generally everyone does have an equal chance of being selected. But that is only true if everyone has the chance of being selected. By which I mean, it could be the case that one of the strata was so small that no one is chosen from that strata.
e.g. Choosing 100 people from a population of 100000 by stratified sampling with two strata: male and female. If there were only 20 males and 99980 females then 0 males would be chosen - so if you were a male you would have no chance of being selected.
Is this correct?
(Afterall, the method does mathematically give everyone an equal chance of being selected - the problem is that you cannot have a decimal number of people)
A secretary of a club with 120 branches and wants to collect a representative sample. She has a complete list of members classified by branches. She selects 4 branches at random and then 10 members at random from those 4 branches.
1. Would all members be equally likely to be chosen? Explain
2. Under what unlikely circumstances would all members be equally likely to be chosen?
I have few ideas on this question. Any help?