When could the sampling error be zero?

Answer 1

I believe you are considering the sampling error as calculated from data. I will give you some examples: If you get the exactly same response from all participants in a survey, you will calculate zero sampling error. For example, if I ask 10 people if Obama Barack is the President of the US, I would probably get 10 "yes" responses. Now the answer was well known, so I would expect very few "no" response. If your measurements are not very sensitive or are recorded with a lack of precision, then there can be zero sampling error. For example, I take the body temperature of students at the college and consider any temperature from 97 to 99 degree F to be normal. I find all students in my sample have normal temperatures. So, zero sampling error can occur because a) sample is small, b) variation in response is either non-existent or very small. In theoretical calculations, where sample error is based on the probability distribution of the population, one can calculate for discrete variables, the probability that a sample error will be zero.