Question

The Business department of a college desires to survey a sample of students taking business statistics. The department is offering 30 classes of business statistics, similar in class size with a total of 1,200 students. They would like the sample size to be roughly 10% of the population of the business statistics students this semester. Describe how might the department obtain a sample using simple random sampling, stratified sampling, and cluster sampling.

Answer 1

Describe how might the department obtain a sample using simple random sampling, stratified sampling, and cluster sampling.-

1. Simple random sampling is a sampling technique where every item in the population has an even chance and likelihood of being selected in the sample. Here the selection of items completely depends on chance or by probability and therefore this sampling technique is also sometimes known as a method of chances.

population size = 1200 and sample size = 10% of 1200 = 120

Now, probability of selecting one unit = 120/1200 = 0.1

So, from all the 1200 students randomly 120 students will be chosen where each one will have equal probability of getting selected without any criteria.

SRS without replacement will be followed

It will rule out bias.

2. In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation independently.

So, here studnets can be divided into various stratas like 'IQ', 'scores in examinations', their major subject etc.

Then, 10% students can be selected from each Strata

E.g. strata are:

Scoring below 40 : size = 100 students, Scoring between 40-60 : size = 400 students , scoring 60-80 : size = 500 students and Scoring above 80: size = 200 students

These are 4 strata then from each strata we will select 10% i.e, 10, 40, 50, 20 students respectively.

3. Cluster sampling is a sampling plan used when mutually homogeneous yet internally heterogeneous groupings are evident in a statistical population. It is often used in marketing research. In this sampling plan, the total population is divided into these groups and a simple random sample of the groups is selected.

Similarly as stratified sampling, we create here groups and then do simple random sampling.

Here, unlike stratified sampling, groups will be

E.g., Students scoring under 40 will also have segregation based on other factor like their major subject.

Here we will have higher no. of groups and more combinations of category which will allow us to better achieve a true sample.

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