Final answer:
A simple random sample from a process or population ensures each element is selected independently and comes from the same population, providing each element with an equal chance of selection and keeping the probability constant. This method helps ensure the sample is representative of the whole population.
Step-by-step explanation:
A simple random sample from a process or an infinite population is a sample that adheres to certain criteria. To answer a student's question: a simple random sample is one in which each element is selected independently, and it ensures that each element selected comes from the same population. The characteristics of a simple random sample include:
- Each element in the population has an equal chance of being selected.
- Each selection is made independently of the others.
- The probability of being selected remains constant throughout the sampling process.
- The method of selection should not introduce any bias.
Samples must be representative of the population to ensure that study findings are generalizable. Sampling without replacement indicates that once an element is selected, it cannot be chosen again, making the events dependent. Various random sampling methods exist, like stratified sampling, cluster sampling, and systematic sampling, which have their own specific applications and advantages.
The principle behind random sampling is to ensure that each member of the population has an equal opportunity to be included in the sample, which helps in generalizing the results to the entire population.