An animal rescue center wants to
find out if people in its town think more money should be spent on animal
welfare. They plan to ask a random sample of
their visitors and volunteers to fill in a questionnaire. Why would their sample not be
representative of the town’s population? Option (A) people will not want to
spend time filling in the questionnaire. Option (B) the center’s visitors
and volunteers are likely to be supportive of spending on animal welfare. Option (C) we do not know how they
will ensure that the sample is random. Or option (D) there might be a high
proportion of children in the sample, which will skew the result.
A sample is representative of the
population if the sample and the population share similar distributions of
characteristics which are relevant to the variable of study. The population here is the people
living in the town. The variable is the spending on
animal welfare. So why is the sample of people at
an animal rescue center not representative?
To understand this, we will really
need to consider the characteristics of people who visit and volunteer at the animal
shelter. These people will be in general
people who like animals. Visitors and volunteers at the
animal shelter will be the people who help animals and will be more likely to think
that more help and money should be spent on animal welfare. Therefore, the statement that the
center’s visitors and volunteers are likely to be supportive of spending on animal
welfare will be the best statement.
But let’s have a quick look at some
of the other options we were given. The statement in option (A) says
that people will not want to spend time filling in the questionnaire. This statement could potentially be
said about any sample group. Even if a random sample of the
town, which is the population, was given questionnaires, there will always be a
problem with this. This is a problem with the method
of data collection but not the representation of the sample.
Next, let’s look at option (C),
which states that we do not know how they will ensure that the sample is random. Well, even if the rescue center
randomly selects from the visitors and volunteers, the problem is that they are
selecting from a restricted population, because they’re sampling only from the
visitors to the shelter and not from the entire town, which is the population.
Option (D) is very similar because
it doesn’t address the problem with the fact that it is only the volunteers and
visitors at the shelter who are asked. Regardless of whether the sample is
taken from people in the town or, in this scenario, at the shelter, if only adults
and children over a certain age should be asked, then measures should be taken to
exclude those children who should not be asked.
And so the statement which best
describes why this sample is not representative of the town’s population is that
given in option (B).