Question

The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 6009 employees at the company and wants to conduct a systematic sample of size 50.

​(a) What is k​?

k= 120

(b) Determine the individuals who will be administered the survey. Randomly select a number from 1 to k. Suppose that we randomly select 4. Starting with the first individual​ selected, the individuals in the survey will be _, _, _,..._.

Answer 1

If the population size is N and we want to draw a sample of size n by Systematic sampling Technique. We know that in a systematic sampling, the first unit is select at random & then the rest of the unit is selected by pre-determined rule. In this technique,

a) N=nk. k=N/n = 6009/50 = 120.18~120

b) Now you can consider a random number between 1 to k. Put a number 1 to N=6069 to each observation of population Let us take a random number, i=40 then the sample of size 4 can be drawn as, 40th, 40+120=160th, 160 +120=280th, 280 + 120=400th observation of population.

Thus, individuals in the sample are 40th, 160th, 280th, 400th employees of the population as mentioned the number from 1 to 6069.