Question

1. Suppose you would like to do a survey of undergraduate students on your campus to find out how much time on the average they spend studying per week. You obtain from the registrar a list of all students currently enrolled and draw your sample from this list.

a. What is your sampling frame?

b. What is your target population?

c. Explain how you would draw a simple random sample for this study.

d. Assume that the registrar’s list also contains information about each student’s major. One could then select a stratified random sample, stratifying on major. What main benefit can result from using a stratified random sample instead of a simple random sample? Would you expect this benefit to be obtained by stratifying on major? Explain.

e. How might you obtain a cluster sample? When should you consider using this type of sampling design?

f. Which type of sampling design is most appropriate for this research problem? Explain.

Answer 1

a) the sampling frame is the list of all the students.

b) the target population is the undergraduate students.

c) In the list of all the undergraduate students assign each student an integer number. for instance, if there are total 150 undergraduate students then each student will receive a number 1,2,...,150. then using the random number table or any software generate n integer numbers generated from uniform distribution (N=150). where n is the sample size which is predetermined as per the time and cost factor. (n can also be decided using probability theory by specifying the precision you require while estimating the mean study time. but for this you will have to conduct a pilot survey first.)

d) By stratifying random sample one can estimate the mean study time with greater precision. for instance, A biology major student might be spending more time on studying than a student whose major is mathematics or commerce.

e) You can form several clusters of undergraduate students then some of the clusters are drawn and surveyed completely for the further study. when there is large variation/heterogenity within the clusters but they are homogeneous among themselves one can use the cluster sampling.

f) cluster sampling may not be suitable as it will not be easy to form heterogeneous clusters. For example suppose if the major is treated as a cluster then some of the majors will be missed completely if the cluster sampling is adopted. therefore stratified sampling, stratifying on majors, will be appropriate.