Question

A college has been given a sizable grant: enough to build either a new library or gymnasium. But, as there is only money enough to build one facility, the president wants to ask students which one they feel is in greater need of renovation. Suppose there are 500 male students and 400 female students in the school.

What is the population under study? (2 points)

The president wants to randomly ask 50% of the students. How many students would this be? (2 points)

Now the president wants to keep the correct proportion of female to male students in the sample. What type of sampling method would be used here? How many girls would be selected? (4 points)

What is the level of measurement for the students’ response? (2 points)

Answer 1

Population under the study is the male and female students in the school.

Total number of students = 500 + 400 = 900

As president wants to randomly ask 50% of the students, he would select 900/2 = 450 students randomly from the population.

Sampling method used here will be stratified random sampling with proportional allocation.

The Population of students are divided into two strata (Male Students and Female Students) and then sample are randomly drawn from each strata with sample sizes that are in proportion to their size.

Like here, number of Population units = 900

Proportion between the number of male and female Students = 500/400 = 5:4

Sample size needed here is n = 900/2 = 450

So, the sample size for male students = (500/900)*450 = (5/9)*450 = 250

Sample size for female students= (4/9)*450 = 200

So, that proportion of sample size of both strata = Proportion of Population size of both strata = 5:4

Student's response will be choosing one from library and gymnasium which they feel is in greater need of renovation.

So, we have two qualitative variables (library and gymnasium) which can not be ranked and hence, are nominal level of measurement.