Question

A local university wants to conduct a sample of 200 students out of 6000 students. We can assume that the university maintains a good roster of all registered students. (1) how would you select the 200 students(a) using simple random sample method and (b) systematic sampling method? (2) suppose that the university administration wants to make sure in particular students who major in music (a small department with only 8% of students major in music)be adequately included in your sample, how would you go about selecting a sample ?

Answer 1

(1)(a) Simple random sampling

In this case the well maintained roster of all registered students are to be obtained and all 6000 students are to be assigned a predetermined unique number between 0001 to 6000. Now randomly selecting 200 4-digit numbers from the random number table and considering the student alongside each number in the sample.

(b) Systematic sampling

In this method any number must be chosen randomly between 001 - 200. The student alongside this number in the roster and then every 6000/200 = 30th student in the register must be chosen till the roster exhausts.

(2) Quota Sampling

This is a non-probabilistic method of obtaining samples. To ensure that the music department gets adequately represented we must decide from before how much proportion of representation they must get and then solely randomly select that many students in the sample from the music department. Then the rest of the sample can be selected from the students of the remaining departments in a random sample approach. The music students in the roster can be struckout and every time a random number corresponding to a music student comes up we can select another random number in place of it until a non-music student gets selected.