Video Transcript
Why does the statement “All the
clothing produced by a factory to measure the quality of that factory” not describe
a simple random sample? Option (A) because this is a simple
but not random sample. Option (B) because a sample has to
be part of the whole population and not the population itself. Or is it option (C) because a
sample is always larger than the parent population?
In this question, we need to
determine why a given statement does not describe a simple random sample. And to do this, let’s start by
recalling what this means. We say that a simple random sample
is a sample in which every member of the population is equally likely to be chosen
for selection. This means that there are two
conditions for a simple random sample. First, we must choose a sample,
which we can also recall is a strict subset of the population. So, it cannot be the entire
population. Second, we need to make sure that
every member of the population is equally likely to be chosen for the sample. If we look at the given statement,
we can note that we are choosing to use all of the clothing produced at the factory
to measure the quality of the factory.
If we consider the two requirements
for this to be a simple random sample, we can note that choosing the entire
population does not give us a strict subset of the population. So this is not a sample. However, we can note that all of
the members have the same probability of one of being chosen. This means that the only correct
answer is option (B). The given example is not a simple
random sample because all samples must be strict subsets of the population. We cannot choose the entire
population.
