Question

Systematic random samples are often used to choose a sample of apartments in a large building or dwelling units in a block at the last stage of a multistage sample. An example will illustrate the idea of a systematic sample. Suppose that we must choose 5 addresses out of 125. Because 125/5=25, we can think of the list as five lists of 25 addresses. Choose 1 of the first 25 at random, using software or Table B. The sample contains this address and the addresses 25, 50, 75, and 100 places down the list from it. If 13 is chosen, for example, then the systematic random sample consists of the addresses numbered 13, 38, 63, 88, and 113.

(a) A study of dating among college students wanted a sample of 200 of the 8000 single male students on campus. The sample consisted of every 40^th name from a list of the 8000 students. Explain why the survey chooses every 40^th name.

(b) Use software or Table B at line 112 to choose the starting point for this systematic sample.

Answer 1

(a)

200 students needed to be selected out of 8000. So, 8000/200 =40. Thus, the survey chooses every 40th name.

(b)

The starting point for this survey is: 04, i.e., 4th name is selected first and then every 40th name is to be selected. So, 4, 44, 84, 124,........

Last name (200th student: n =200) to be selected following this sequence which is in Arithmetic Progression is: t_n =a+(n-1)d =4+(200 - 1)*40 =4+199(40) =4+7960 =7964th name.

So, the sequence is: 4, 44, 84, 124,...........,7964.

(since in Table B below, along the line 112, we have first two digits of 59 in first column which is greater than 40, we have 88 in the second column >40 and then in the third column, we have 04 <40. So, we selected 4th name as a starting point).

(If we have selected 59th name first. Then, our last term (n =200) of the sequence will be: a+(n-1)d =59+119(40) =59+7960 =8019th name but we have only 8000 students. So, we need to select 40 or less as the starting point because if select 40, last term will be: 40+199(40) =8000 and less than 40 as a starting point leads to last term of less than 8000).

(So, we can also use random number generator between 1 and 40(inclusive) to select the starting point).