What type of random sample should
be used to determine the subject preferences of a group of 400 students given the
ratio of males to females is three to two. Is it A) a simple random sample or
B) a stratified random sample?
Let’s begin by recalling the
definition of these two types of sampling methods. A simple random sample is a subset
of a population, and remember the population is everyone, in which every single
member of this subset has an equal probability of being chosen. It’s meant to be an unbiased
representation of a group.
For example, we could choose a
simple random sample of 30 students in a school of 400 by assigning a number to
every student and using a random number generator to generate 30 numbers. It’s considered a fair way to
select a sample though it doesn’t guarantee that the sample itself will be
representative of the whole population.
A stratified random sample involves
dividing the population into smaller groups, which are known as strata. These groups are based on specific
shared attributes, for example, age or gender. Each member of the subgroups then
have an equal probability of being chosen. But these probabilities might be
different from subgroup to subgroup. And this method can be beneficial
as it ensures a representative sample though strata must be carefully defined to
ensure that there’s no overlap.
Now, let’s consider the population
we’ve been given. We’re told that the population is
400 students. We’re also told that the ratio of
males to females is three to two. This indicates to us that our
sample needs to be truly representative of this breakdown. To ensure that this is the case,
we’re going to use stratified random sampling. And as a little aside, we can use
proportion to work out how many students would be in a sample.
Since the ratio of males to females
is three to two, we can add three and two. And we can see that our population
is broken down into five parts. Three of these parts represent the
proportion of male students. So three-fifths of the population
must be male. And two-fifths must be female. So we would need to ensure that
three-fifths of a sample are males and two-fifths of that same sample are