Video Transcript
A teacher wants to know the
favorite subject of the students in his school. Since the school has 300 students,
he decides to only ask a sample of the population. For which of the following sampling
methods does each student not have an equal probability of being chosen for the
sample? Option (A) a sample of 30 students
who are chosen by selecting 30 national IDs randomly. Option (B) a sample o f 30 students
selected by writing names of students in small papers, folding the papers, placing
the papers in a bowl, and drawing 30 pieces of paper. Option (C) a sample of 30 students
selected by putting students’ names in a list, giving each name a random number from
one to 300, and choosing the names that have numbers divisible by 10. Or option (D) a sample of 100
children who have blue eyes.
We begin by recalling that a simple
random sample is a sample of the population such that every member of the population
has an equal chance of being selected for the sample. This means that we need to
determine in which of the four given options does every student have the same
probability of being chosen for the sample and which options do not have an equal
probability for every student.
Let’s start with option (A). Here, students are chosen randomly
by their national ID. We may worry that national IDs may
not be random, which could well be true. For example, twins would likely
have sequential ID numbers. However, we choose 30 students by
randomly selecting 30 IDs from the list of 300. And in this way, every ID on the
list has an equal chance of selection. Option (A) then represents a simple
random sample. And we can eliminate this since
we’re looking for sampling methods where each student does not have an equal chance
of selection.
In option (B), we have a similar
story. Every student’s name is written on
a piece of paper, the papers are shuffled in a bowl, and 30 are drawn at random. Of course, with 300 students, we
might need quite a big bowl. Nevertheless, since the 30 pieces
of paper are drawn randomly, every student has an equal chance of selection. We can therefore eliminate option
(B), since this is a simple random sample and every student does have an equal
chance of selection.
Option (C) is quite similar in that
this time each of the 300 students’ names are listed and then randomly allocated a
number from one to 300. The sample then consists of the
names that are allocated a number divisible by 10. And there will be 30 of these. Since the allocation of numbers to
names is random, each student has an equal chance of being allocated a number
divisible by 10. Hence, this is a simple random
sample, and we can eliminate option (C).
Finally, in option (D), the sample
consists of 100 children who have blue eyes. This means that any student who
does not have blue eyes has zero chance of being selected for the sample. So this is not a simple random
sample, and this is our answer. Option (D) is the only sampling
method where each student does not have an equal probability of being chosen for the
sample.
