Question

(8 points) A statistics student at a small liberal arts college who is curious about the relationship between the amount of time students at his college spend on social networking sites and their performance at school decides to conduct a survey. Four research strategies for collecting data are described below. In each, name the sampling method proposed and any bias you might expect.

Strategy 1: He obtains a list of the 1500 students at the college. He chooses a random number kk between 1 and 15 and then samples that person and every kkth person on the list. He emails the survey to each of the people in the sample and asks them to complete it by next Friday.

1. What is the sampling method?

A. Cluster sampling
B. Systematic sampling
C. Simple random sampling
D. Stratified sampling
E. Convenience sampling

2. What type of bias would you expect? (check all that apply)

A. No bias in this survey
B. Response bias
C. Nonresponse bias
D. Selection bias

Strategy 2: He gives out the survey only to his friends, and makes sure each one of them fills out the survey.

3. What is the sampling method?

A. Systematic sampling
B. Simple random sampling
C. Stratified sampling
D. Cluster sampling
E. Convenience sampling

4. What type of bias would you expect? (check all that apply)

A. Selection bias
B. Response bias
C. Nonresponse bias
D. No bias in this survey

Strategy 3: He randomly chooses 3 floors of the largest dorm on campus and distributes a paper survey to each resident on those floors. He places a box in the common room of the dorm to collect the completed surveys.

5. What is the sampling method?

A. Cluster sampling
B. Convenience sampling
C. Systematic sampling
D. Stratified sampling
E. Simple random sampling

6. What type of bias would you expect? (check all that apply)

A. Response bias
B. Selection bias
C. Nonresponse bias
D. No bias in this survey

7. Which strategy will give him the most representative sample of students at his college?

A. Strategy 1
B. Strategy 2
C. Strategy 3

Answer 1

1. The sampling method selected in Strategy 1 is Systematic Sampling. Therefore, option B is correct In Systematic Sampling, the population units are arranged in some order and the first unit of the sample is selected randomly from the ordered units and the other units in the sample are selected according to a prespecified number called sampling interval. The sampling interval is denoted by k, where k is obtained by dividing the total population by the sample size. Then the next unit in the sample is every k1" unit from the first selected unit Here, in strategy 1, the student selects randomly a student between 1 and 15 among 1500 students and then selects every k" population amongst the students. Therefore, the technique used for sampling is systematic sampling. 2. The bias that can be expected in Strategy 1 could be the Nonresponse Bias. Therefore, option C is correct Since the student has mailed the survey to each of the selected students in the sample and asked them to send it by next Friday, there may be chances of nonresponse bias. There are chances that the student may forget to fill the survey, or the student might ignore the survey, or it might be possible that any student did not get time to fill the survey due to the busy schedule, therefore, all these reasons will lead to nonresponse and will lead the survey to a biased survey. 3. The sampling method used in Strategy 2 is Convenience Sampling. Therefore, option E is correct

Convenience Sampling is a sampling technique in which sampling units are selected according to the convenience of the researcher, that is, those units are included in the sample which are easy to approach. Here also in Strategy 2, the student has given the survey only to his friends who are obviously easy to approach. Thus, it can be said that the sampling technique used is Convenience Sampling 4. expected in Strategy 2 will be the selection Bias. Therefore, option A is correct The Since the student is collecting information only from his friends which means that the units in the sample selected are not random and this sample will not represent the population well 5. The sampling method used in Strategy 3 is the Cluster Sampling. Therefore, option A is correct In cluster sampling, the entire population is divided into different groups or clusters and then from each cluster, a random sample is drawn, or the investigator may study the entire cluster Here also in Strategy 3, the student has chosen 3 floors from the largest dorm on the campus and then he surveys each resident on each floor. Therefore, the student has used the concept of cluster sampling 6. The bias expected in Strategy 3 would be the non-response bias. Therefore, option B is correct The student placed a box in the common room of the dorm and asked each resident to fill the survey and submit the survey paper in that box, therefore, this may lead to nonresponse. The residents may ignore, or they might not fill the survey intentionally understand some of the questions asked in the survey. All these cases will lead to nonresponse they might not or

7. Strategy 1 will give the student fhe most representative sample of students at his college he is selecting the sample from the list of 1500 students. Therefore, option A is correct as