Question

Use the following study question and population to write how someone would sample the population in order to obtain a representative sample. Explain a way sample using each sampling technique ( simple random sample, cluster sample, stratified sample, systematic sample)

What is a typical student at “X” college?

Population: all students enrolled at X college taking college credit classes.

Paper needs specifics about each sampling method and described in details, using values for the population and the sample size ( made up values). Also include an introduction describing the study question and population to be studied. Determine the best method of sampling that would be best in order to collect a representative sample and why.

Answer 1

For the given scenario, we are given a population as the all students enrolled at X college taking college credit classes. From this population we have to select the random sample by using different sampling techniques. For this scenario, a typical student at ‘X’ college is a sampling observation. Let us see how to use different sampling techniques for the selection of a random sample.

Simple Random Sample:

In simple random sample, we select the required random sample by using random numbers. These random numbers can be generated by using various methods such as spreadsheets, statistical softwares, calculators, random number tables, etc. We will assign student ID’s to all students under population and then we will select some random ID’s for selection of random sample.

Cluster random sample:

In cluster random sample, we first divide the entire population into separate groups or clusters and then we select some clusters randomly. For the given scenario, we will divide the population of all students into different groups or clusters according to their classes. We consider class as a cluster. Then we will select some clusters or classes randomly. We will use all students in the randomly selected clusters for making a random sample.

Stratified sample:

In stratified sample, we divide the population into groups and then we select some observations from each group by using simple random sampling. For the given scenario, we will divide population of all students according to their classes. We would consider each class as a stratum. Then we will use simple random sampling for the selection of some students from each classes. In this way, we can use stratified sample for selection of stratified random sample.

Systematic sample:

For the given scenario, we will assign numbers from 1 to n for students under population. Then we will select first number or observation randomly and then after we will select the numbers by using specific distance from the randomly selected observation at first time. Suppose, first random observation is 7 and specific distance is 5, then random observations will be 7, 12, 17, 22, 27, 32, ..etc. The specific distance is depends on the sample size required.