Question

Question 1: A study is to be conducted to examine how much currently-enrolled students at a particular university feel their academic program is relevant to their livelihood goals. Each student sampled is asked to provide a score on a scale from 0-10, with 1 signifying that their program is of minimal relevance, and 10 signifying that their program is of maximal relevance.

a) Describe the relevant population for this study.

For each of (b)-(f), which are different approaches to collecting a sample for this study, answer the following: i. What type of sample is being conducted, and why? ii. Is the sample biased or non-biased, and why? Note: in each case, individuals selected are included in the sample only if they are currently-registered students at the university.

b) From a list of all currently-registered students at the university, a sample of students is selected randomly.

c) Based on current enrolment levels in each program area at the university, a random sample is selected such that each program area is proportionally represented in the sample.

d) From a similar list as in (b), every 100th currently-registered student at the university is selected, starting at a randomly-selected position in the list between 1 and 100.

e) An email survey is sent to every currently-registered student at the university, and a sample is obtained from the first 100 students who submit a completed online response form.

f) A similar list as in (b) is divided, based on alphabetical order, into 40 equal-sized groups. Then, 5 of these groups are randomly selected, and every student in each selected group is included in the sample.

Answer 1

A study is to be conducted to examine how much currently-enrolled students at a particular university feel their academic program is relevant to their livelihood goals. Each student sampled is asked to provide a score on a scale from 0-10, with 1 signifying that their program is of minimal relevance, and 10 signifying that their program is of maximal relevance.

a) the relevant population for this study

Currently-enrolled Students at a particular university are the relevant population. Collection of values of “SCORES provided by the students” will be the data. Population size=N.

b) From a list of all currently-registered students at the university, a sample of students is selected randomly.

i. Type of sample being conducted: SRSWOR- Simple Random Sampling Without replacement Because a sample of size n selected from population of size N randomly without considering program area.

ii. Sample Biased/Non-Biased: Sample may be Non-biased (SRS). (Note: In Sample consecutive random numbers may be generated which means one or more student in the same program may be included.)

c) Based on current enrollment levels in each program area at the university, a random sample is selected such that each program area is proportionally represented in the sample.

i. Type of sample being conducted: Stratified Random Sampling under proportional allocation. “Each program” will form a stratum. Let k= number of strata. Ni is number of sampling units (current number of Students enrolled in particular program) in the i^th stratum (i^th program). ni=number of sampling units to be drawn from i^th stratum by SRSWOR. n=size of stratified sample. Proportional allocation- because each program area should be represented in the sample.

ii. Sample Biased/Non-Biased: Stratified sample is highly representative of the population. Overlapping can be an issue if there are subjects-students that fall into multiple subgroups(programs).

d) From a similar list as in (b), every 100th currently-registered student at the university is selected, starting at a randomly-selected position in the list between 1 and 100.

i. Type of sample being conducted: Systematic Sampling because “i (< = k)”=random start= a random number selected by SRS (Simple Random Sampling) from 1 to k i.e.1 to 100. Unit corresponding to this number is selected and subsequently every k^th unit is selected. Systematic sample of size n will consist of the units i, i+k, i+2k,….,i+(n-1)k i.e. i,i+100,i+200,……,.i+100(n-1).

ii. Sample Biased/Non-Biased: If we can assume that the population list is randomly shuffled, then systematic sampling is equivalent to simple random sample, where there is no bias.

e) An email survey is sent to every currently-registered student at the university, and a sample is obtained from the first 100 students who submit a completed online response form.

i. Type of sample being conducted: Random sampling & Convenience Sampling (convenient- a sample obtained from first 100 students who submit form).

ii. Sample Biased/Non-Biased: Biased as it may happen that all the students of particular program may fill the form. Underrepresentation OR Overrepresentation may occur.

f) A similar list as in (b) is divided, based on alphabetical order, into 40 equal-sized groups. Then, 5 of these groups are randomly selected, and every student in each selected group is included in the sample.

i. Type of sample being conducted: Cluster sampling. Here, 40 clusters (equal-sized groups) are present. 5 clusters are to be selected. Every student in each selected group is included in the sample.

ii. Sample Biased/Non-Biased: may or may not be Biased. (Population of size N is divided into 40 clusters of size N/40. It may happen consecutive clusters are selected. List of alphabetical order may contain students with same alphabet-same program-same livelihood goals.)