Simple Random Sample vs Sample
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Simple random sample
Collecting data and study design
A simple random sample is selected so that every possible sample of the given size has an equal chance of being the one chosen.
In a simple random sample, often shortened to SRS, each individual and each group of individuals is equally likely to be picked. For example, numbering all 500 students at a school and using a random number generator to select 30 of them produces an SRS. This equal-chance selection removes selection bias and is what justifies the standard error formulas used later in inference. It usually requires a list of the whole population to sample from.
Sample
Collecting data and study design
A sample is the subset of a population that you actually collect data from in order to estimate something about the whole population.
Because measuring an entire population is often impossible, you gather data from a smaller sample and use it to make estimates. For example, polling 1,000 voters to estimate how all voters will act treats those 1,000 people as the sample. A numerical summary of a sample, such as the sample mean (written , read as x-bar), is called a statistic. A well-chosen random sample lets that statistic stand in for the unknown population value.