Video Transcript
Which of the following would result
in a simple random sample? Option (A) 10 dogs of different
types selected to study the effects of animals living underwater on a submarine. Option (B) a liter of drinking
water taken from 100 random households in a city to measure the level of drinking
water pollution in the city. Option (C) a list of temperature
measurements on every weekend in Cairo for the past year selected to study climate
change in that year. Or option (D) all soccer players in
a country selected to study the players’ daily routine.
We’re asked to determine which of
the given options would result in a simple random sample. So let’s begin by reminding
ourselves of what we mean by this. Recall that a population is defined
as the entire set of objects we’re analyzing. And a sample is defined as a
smaller subset selected from the population, where the size of this subset is the
sample size. And finally, a simple random sample
is a sample taken from a population where every member of that population has an
equal chance, or probability, of being selected for the sample. Okay so now we know what a simple
random sample is, let’s look at each of the given options in turn and see if they
match our definition.
Beginning with option (A), we have
10 dogs of different types selected to study the effects of animals living
underwater on a submarine. The first thing we can note is that
our population is animals. The study is on the effects of
living underwater on animals. Dogs, of course, are a type of
animal. And we definitely have a sample,
since only 10 are selected. But even though there are 10
different types of dog selected, choosing only dogs to represent the population of
animals means we can’t make any observations about any other type of animal.
So the sample of 10 dogs giving us
a sample size of 10 does not represent the population of animals. And the fact that only dogs were
selected from all animals means each type of animal did not have an equal chance of
selection. So option (A) does not result in a
simple random sample.
Now looking at option (B), we have
a liter of drinking water taken from 100 randomly selected households in a city. We can identify our population as
all households in the city. Our sample size is 100, and our
sample consists of the 100 randomly selected households. Now the fact that these 100
households were selected randomly from the whole population of households in the
city tells us that each household had an equal chance of selection. And therefore, the sampling method
described in option (B) would result in a simple random sample. So option (B) is a simple random
sample, but we still need to consider options (C) and (D).
Looking at option (C) first, the
sample described is a list of temperature measurements taken every weekend for one
year. And as there are 52 weeks in one
year, our sample size will be 52. Now we would expect the population
in this case to be temperature measurements across the whole year. So the question now is, is our list
of weekend temperatures a simple random sample? By only listing weekend temperature
measurements, did each day in the year have an equal chance of selection? Our answer to this must be no,
since by only choosing weekend days, temperature measurements taken on any weekday
had no chance of selection. So not all members of the
population of temperature measurements had the same chance of selection. And therefore, we can eliminate
option (C). This is not a simple random
sample.
Finally, in option (D), we have
that all soccer players in a country are selected to study their daily routine. In this case then, the population
is actually all the soccer players in the country. And since the entire set of players
were selected, no smaller subset representing a sample of players was selected from
the population. Since no sample was selected, there
is no possibility that a simple random sample could result in option (D). Hence, we can eliminate option
(D). And we see that only the sampling
method in option (B) would result in a simple random sample.
