Question Video: Calculate the Sample Size of a Stratum Given the Sample Size of the Other Stratum and the Population Size Mathematics

Video Transcript

Ethan needs to conduct a study to determine whether the students in his school like playing football. He decides to divide the students into two groups, boys and girls, knowing that the school has a total of 200 students, 80 of whom are girls. If Ethan decides that his sample size will be 50, how many girls should he select for the study?

Since the population of students is split into two distinct strata, that is, boys and girls, the appropriate sampling method is stratified or layered random sampling. A stratified random sample is a sample consisting of random samples selected from distinct groups or strata within the population. The sample size for each stratum reflects the stratum proportion of the population.

In order to calculate the sample size for a particular stratum, that is, lowercase 𝑠, we use the formula lowercase 𝑠 is equal to uppercase 𝑆, which is the number in the stratum, divided by the number in the population, uppercase 𝑁, multiplied by lowercase 𝑛, which is the overall sample size. In our case, we have a total of 200 students so that uppercase 𝑁 is 200. We know that we have 80 girls so that uppercase 𝑆 is equal to 80 and that Ethan’s sample size is 50. That is, lowercase 𝑛 is equal to 50. And our sample size for girls is 80 over 200 multiplied by 50, that is, 80 girls divided by a population of 200 multiplied by the sample size 50. We can divide numerator and denominator by 50 and again numerator and denominator by four, which gives us 20. Therefore, Ethan should select 20 girls for his study.