Video Transcript
If a random sample is taken from a
population where each member of the population is replaced after selection, can this
sample be considered to be a simple random sample?
In this question, we are told that
a random sample is taken of a population where each member of the population is
replaced after selection. We want to determine if this is a
simple random sample.
To begin, we can recall that a
simple random sample is a sample in which every member of the population has the
same probability of being chosen. Therefore, there are two things
that we need for this to be a simple random sample. First, we need the selections to
form a sample, which means that we do not select the entire population. Second, we need every member of the
population to have the same chance of being chosen.
We are told that we take a random
sample from a population with replacement. We can note that if our original
population is chosen at random, then every member of the population has the same
chance of being chosen. So, we can say that yes, this can
be considered to be a simple random sample.
