Can you please give the more appropriate answer of this question with example? A population is divided into several clusters and it has been found that all the items within a cluster are alike. Which of the sampling procedure would you adopt? Give appropriate reasons for selecting such method.

Introduction:
The procedure or process of taking a sample from the population is is called sampling. In general we have different type sampling techniques to take sample from the population. Following are the some important sampling techniques
1. simple random sampling
2. systematic sampling
3. stratified random sampling
4. Cluster sampling
Before going to answer the above question must know about the difference between stratified random sampling and Cluster sampling
Stratified random sampling:Stratified random sampling is a method of sampling that that involves dividing the whole population into smaller sub groups we called as strata or cluster and selecting the samples from each strata. we aim at securing homogeneity within subgroups and heterogeneity between subgroups.
1.Here units or items in each group are as homogeneous
2. The group means are as heterogeneous as possible
Cluster sampling: Cluster sampling also is a method of sampling that involves dividing the whole population into smaller subgroups we called as cluster and selecting the samples from each cluster. We aim at securing heterogeneity within subgroups and homogeneity between subgroups.
1.Here units or items in each group are as heterogeneous
2. The group means are as homogeneous as possible
The only difference between cluster and stratified random sampling.For the Stratified random sampling all the items within a strata or cluster are homogeneous or similar or alike. Where as for cluster sampling all the items within a strata or cluster are heterogeneous or dissimilar
From the above question we observed that A population is divided into several clusters and it has been found that all the items within a cluster are alike. the all items in within a cluster are similar in such cases the Stratified random sampling is the appropriate method to use
The following is the example for the Stratified random sampling
A research team has decided to perform a study to analyse the grade point averages or GPAs for the 10 million college students in the U.S. The researchers decide to take a random sample of 4,000 college students within the population of 10 million. The team wants to review the various majors and subsequent GPAs for the students or sample participants.
The 4000 college students divided into smaller subgroups and the items in each cluster are similar the following are the subgroups
1.English: 560 2. Science: 1135 3.Computer science: 800 4. Engineering: 1090 5. Math: 415
The each cluster or subgroup contains similar same subject students only
The researchers have their five strata from the stratified random sampling process. Next, the researchers study the data of the population to determine the percentage of the 21 million students that major in the subjects from their sample. The findings show the following:
1. 12% major in English 2. 28% major in science 3. 24% major in computer science 4. 21% major in engineering
5. 15% major in mathematics
The team decides to employ a proportional stratified random sample whereby they want to determine if the majors for the students in the sample represent the same proportion as the population.
However, the proportions in the sample are not equal to the percentages in the population. For example, 12% of the student population are English majors, while 14% of the students in the sample are English majors (or 560 English majors / 4,000).
As a result, the researchers decide to resample the students to match the percentage of majors in the population. Out of the 4,000 students in their sample, they decide to randomly select the following:
1. 480 English majors (12% of 4,000) 2. 1,120 science majors (28% of 4,000) 3. 960 computer science majors (24% of 4,000) 4. 840 engineering majors (21% of 4,000) 5. 600 mathematics majors (15% of 4,000)
The researchers now have a proportionate stratified random sample of college students and their respective majors, which more accurately reflects the majors for the overall student population. From there, the researchers can analyse the GPAs of each stratum as well as their characteristics to get a better sense of how the overall student population is performing.