Question

When selecting a sample, there are several methods of selection available.

A company with hundreds of employees has hired a third party human resources agency. The agency is to study the employees and their level of job satisfaction, and to discover if the company needs to change anything about its management of human resources.

As part of this study, the agency wants to survey a selection of employees from within the company. Four members of the agency propose four different sampling plans for the survey.

Alvin: 'The marketing department of the company is reflective of the rest of the company in terms of job satisfaction. We should simply survey that department.'

Bonnie: 'We have access to the names of every employee in the company. We should survey 50 people from the company by putting every name in a list and choosing 50 names completely at random.'

Crystal: 'The company is made up of 60% men and 40% women. I believe that men and women will have different levels of job satisfaction, and we should force our sample to have 60% men and 40% women.'

Donald: 'As Bonnie says, we should put every name in a list. However, we should only pick one person at random, from the first ten people on the list, and then pick every tenth person thereafter.'

a)The member that is proposing a cluster sample is:

1) Alvin
2) Bonnie
3) Crystal
4) Donald

b)From the list below, select the correct statement about sampling selection methods:

1) Systematic sampling guarantees that every sample of a given size stands an equal chance of being selected.
2) Stratified sampling guarantees that every sample of a given size stands an equal chance of being selected.
3) Cluster sampling guarantees that every sample of a given size stands an equal chance of being selected.
4) None of the above statements are correct.

A bank has been losing customers over the past year. Whenever a customer closes their account with the bank, they are always asked why (so the bank has some idea of the services that it needs to improve). However, it would like to gather more information on what its current customers think, to see if there are any other areas that it needs to work on.

The bank has 100,000 customers. Every customer name is put into an ordered list, effectively giving each customer a number from 1 to 100,000. The bank then generates 500 unique random numbers between 1 and 100,000 and selects the customers that correspond to these numbers. The bank surveys these 500 customers.

This is an example of:

	systematic sampling
	simple random sampling
	stratified sampling
	cluster sampling

Answer 1

a)The member that is proposing a cluster sample is:

1) Alvin

Whereas Bonnie is proposing a simpke random sampling ( each person in the population has equal probability to be included in the sample)

Crystal is proposing stratified random sampling (dividing the population in two strata viz : men and women)

Donald is proposing systematic sampling.

Note that, In stratified sampling, the sampling is done on elements within each strata. In stratified sampling, a random sample is drawn from each of the strata, whereas in cluster sampling only the selected clusters are sampled. A common motivation of cluster sampling is to reduce costs by increasing sampling efficiency. So, here only that part of the population is focused which is reflective of the rest of the company in terms of job satisfaction (this is a cluster, also cost is reduced here as a part of the population is being studied)

B) option 4 is correct i.e None of the above statements are correct. As it is the simple random sampling which guarantees that every sample of a given size stands an equal chance of being selected.

A sample is a simple random sample if each unit of the population has an equal chance of being selected for the sample. It is the basic sampling technique where we select a group of subjects or a sample for study from a larger group or population. Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. It is also known as ‘unrestricted random sampling’.

C) the given example is an example of simple random sampling. As, Every customer name is put into an ordered list, effectively giving each customer a number from 1 to 100,000 such that every customer gets an equal chance of being included in the sample size of 500 ( property of simple random sampling : every element of population gets an equal chance of being included in the sample)