Question

Determine the individuals who will be administered the survey. Randomly select a number from 1 to k. Suppose that we randomly select 6. Starting with the first individual​ selected, the individuals in the survey will be nothing​, nothing​, nothing​..., nothing.

Answer 1

This is a systematic sampling problem.

systematic sampling: It is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point and a fixed, periodic interval. This interval, called the sampling interval (k), is calculated by dividing the population size(N) by the desired sample size(n).

Here, we are given a problem where we have to select indiviaduals for a survey from N number of individuals having a systematic sample size, n, such that k = N/n

In order to determine the individuals who will be administered the survey, we randomly select a number from 1 to k, in this case the number is 6.

this means, the first individual selected in the survey will be 6 and others will be followed by a gap of k until we reach a number that is less than or equal to the total number of subjects N

i.e., the individuals who will be administered the survey, are:

6, 6+k, 6+2k, 6+3k,........6+mk

such that, 6+mk N where m is positive integer.

To understand this better, consider the following problem as an example:

The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 5780 employees at the company and wants to conduct a systematic sample of size 60.

What is k?

answer: here, N=5780; n=60

we will compute k as:

k = N/n = 5780/60 = 96.33 96 (as sample size must be a wwhole number)

now, the next part of the question:

Determine the individuals who will be administered the survey. Randomly select a number from 1 to k. Suppose that we randomly select 6. Starting with the first individual​ selected, the individuals in the survey will be nothing​, nothing​, nothing​..., nothing.

starting with 6, the individuals in the survey will be:

6, 6+k, 6+2k, 6+3k,........6+mk

i.e., 6, 6+96, 6+2*96,.........., 6+60*96 [as 6+60*96 = 5766 < 5780]

the individuals in the survey for this example will be:

6,102,198,.......,5766

Hope this helped!