Video Transcript
A restaurant owner wants to know if
his guests enjoyed the food served in one evening. He decides to ask some of his
guests. He chooses a sample. Which of the following methods is
considered a random sampling method? Option (A) choosing those who sit
at tables that have even numbers. Option (B) choosing female
guests. Option (C) choosing those who order
chicken. Option (D) choosing male
guests. Or option (E) choosing those who
enter the restaurant after 11 PM.
We’re given five different ways of
taking a sample of the guests in a restaurant, that is, five sampling methods. And we’re asked which of these can
be considered a random sampling method. So let’s begin by defining what we
mean by a random sampling method. We remind ourselves first that a
population is defined as the entire set of objects we’re analyzing or concerned
with. In our case then, we can say that
the population is all of the restaurant’s guests on the evening in question. We then define a sample as a
smaller subset or a selection of the population. A random sample, sometimes classed
as a simple random sample, is a sample where every member of the population has an
equal chance, or probability, of selection. The sampling method is the method
we use to select the sample members from the population.
Let’s consider each of the methods
given in options (A) to (E), starting with option (A). This sampling method selects guests
who sit at tables that have even numbers. Assuming that guests were seated
randomly at the tables in the restaurant on arrival, there should be nothing to
distinguish between guests who sit at even-numbered tables and those who sit at
odd-numbered tables. Since guests are equally likely to
have been allocated an even-numbered table as an odd one to sit at, the method
described in option (A) can be considered a random sampling method.
Now let’s consider option (B),
where the sampling method is to choose female guests. If our sampling method selects only
female guests, then any male guests will have zero chance of selection. The selection is therefore not
random, since we’re excluding any male guests completely from the sample. Therefore, option (B) cannot be
considered a random sampling method. Noting that the same logic applies
in option (D), where instead of female guests, only male guests are chosen, we can
also discount option (D). Option (D) cannot be considered a
random sampling method.
Now let’s go back and look at
option (C). In option (C), only guests who
order chicken are selected. Now if this were a restaurant where
the only thing served was chicken, we could then say that taking a sample of those
guests who order chicken would be considered a random sample. But we’re not given any information
as to what’s on the menu. So we can’t assume that only
chicken is served. Then choosing only guests who order
chicken means that anyone who does not order chicken has no chance of being
selected. All guests do not have an equal
chance of being selected, so the sampling method is not random and we can discount
option (C).
Finally, considering option (E),
where only guests entering the restaurant after 11 PM are chosen, this excludes any
guests who enter the restaurant before 11 PM. All of those guests have zero
chance of being selected, and the chance of being selected is not equal for every
member of the population of guests. This sampling method cannot
therefore be considered as a random sampling method. And so we can eliminate option
(E).
Hence, option (A), that is,
choosing those guests who sit at tables that have even numbers, is the only sampling
method that is considered random.
