Question

A randomized block design was used to study the amount of grants awarded to students at a large university. One block consisted of undergraduate students and the other block consisted of graduate students. Samples of 30 were taken from each block. Could the combined sample of 60 be considered a simple random sample from the population of all students, undergraduate and all graduate, at the university? Explain.

Answer 1

no it can't be taken as a random sample fromthe population of all students.

Here we have divided the total population into two parts graduate and undergraduate students and take 30 random samples from each of them.

If we want to take 60 samples from all the students of the University there is no surety that we will get 30 from each of them we may have got 40 from ug and 20 for g or vice versa.Here we 1st make a group them take samples from it as an example if we are taking samples from graduate we can never get a ug student as a sample after a g student and the other way round.but if we take whole set altogether we can always get a alternating series.

the samples are random with its own group.. This set up is more like a stratified random sampling rather than simple random sampling where the no of strata is 2.