Video Transcript
A scientist decides to conduct a
survey on the effect of a certain medicine in a city of 100,000 people. He divides them into three groups
based on their region: city center, outer city, and suburbs. There are 10,000 people in the
suburbs and 30,000 people in the outer city. If the scientist decides to take a
sample of 1,000 people, how many people from the suburbs should be included?
Since the city is divided into
three distinct groups or strata, an appropriate sampling method is stratified or
layered random sampling. Recall that a stratified random
sample is one which combines a number of separate random samples taken from distinct
groups within the population. The size of the sample from each
group reflects the proportion of that group or stratum within the population.
In order to calculate the sample
size for each stratum, we use the formula lowercase 𝑠, which is the individual
stratum sample size, is equal to uppercase 𝑆, which is the stratum size, divided by
uppercase 𝑁, which is the population size, multiplied by lowercase 𝑛, which is the
overall sample size. In our case, our population size is
100,000. That’s uppercase 𝑁. We’re interested in how many people
from the suburbs should be in our sample. And we’re told that there are
10,000 people in the suburbs. So uppercase 𝑆 is equal to
10,000. Our overall sample size from the
population is 1,000 people so that lowercase 𝑛 is 1,000. Into our formula then, the sample
size for the suburbs is 10,000 divided by 100,000 multiplied by 1,000, that is, the
stratum size divided by the population size multiplied by the overall sample
size.
We can divide the numerator and the
denominator by 1,000 and then again by 100. And we have the sample size of
people from the suburbs is 100. So for a sample of 1,000 people,
100 of those should be from the suburbs.
