A simple random sample of size n from an infinite population should have what characteristic?

A simple random sample from an infinite population should indeed exhibit the characteristic of having the same probability for each possible sample. This means that every possible sample of the same size has an equal chance of being selected from the population. This equality in selection is fundamental to the concept of simple random sampling; it ensures that the sample fairly represents the population, which is crucial for making valid inferences from the sample data.

When sampling techniques do not adhere to this principle, biases can be introduced, and the results of the analysis may not accurately reflect the characteristics of the entire population. Therefore, having the same probability for each possible sample assures that each unit in the population has an equal opportunity to be included in any sample, thereby promoting randomness and validity in the sampling process.