Forty seven math majors, 22 music majors and 31 history majors are randomly selected from 585 math majors, 279 music majors and 393 history majors at the state university. What sampling technique is used?
Answer: stratified
Why is it stratified and not cluster ?? I am having a hard time figuring out a difference
Clusters are essentially partitions of your sample such that each cluster has a mean similar to the entire population, then you randomly sample from a radomly chosen subset of the clusters. Thid double randomization allows you to get a represntative sample with fewer samples. See this link
Stratified sampling is done when there is a heterogenous population with identifiable co-variates (in this case, college major). So you randomly sample from each strata, but the sample size is proportional to fraction of the total population a particular strata represents. That is what is being done in your question.
If it were cluster sampling, then it would be several groups of samples not from each major, but from, perhaps, different dormatories on campus, where dormatories are expected to be similar to each other.