Question

The dean of a four-year university wants to determine how the undergraduates feel about the dining services. There are 10,000 undergraduates at this university that take advantage of dining services, so it would be too expensive to poll every student. Instead, the dean chose to use the following sampling method:

Using the registrar's alphabetical listing of all undergraduates, randomly pick a number between 1 and 100, and count that far down the list. Take that number and every 100th name after it. For example, if the random number chosen is 65, then pick the 65th, 165th, 265th, and so forth, names on the list.

Thoroughly explain and give an example why this method of sampling is not simple random sampling

Answer 1

In a simple random sampling each and every students has equal chances of being selected. That is for 10000 students each should have 1/10000 =0.0001 or 0.01 % chance of being selected.

But here 1st student is choosing by selecting a number from 1 to 100 and then choose the student corresponding to this number. So the students who are in the Top 100s in the registrar have more probability to be choosen in the 1st turn than the students who are below 100.

Again the choosing of the remaining students depends on the number choosen. For example if 65 is choosen then 165th , 265th are sure that they will be choosen. This is a Systematic Sampling method.

This is not Simple Random sampling because they are not randomly choosen at all and probability of each student of being selected is not same for all.