Question

Question 1
(a) What is the objective of sampling? [2]
(b) What is the difference between a poll and a survey? [4]

(c) What is the difference between probability sampling and non-probability sampling? Give exam-
ples of both. [8]

(d) What are the sources of errors in surveys? Explain in detail giving examples. How can the
errors be reduced? [12]
(e) List all possible simple random samples of size n = 2 that can be selected from the population
{0, 1, 2, 3, 4}, and calculate s^2

for the any two samples and show that s^2=(N/N−1)σ^2




. Also calculate

σ^2 for the population and V ar( ̄y) for the two samples.

Answer 1

a. There is an assumption that population is homogeneous (soup has to be mixed well). That sample can be used to infer the characteristics of the population with reasonable accuracy.

Sampling is used to infer the characteristics of the population without having to consider entire population

b. A poll is used to ask one simple question while a survey is generally used to ask a wide range of mutliple questions. The main difference between the two is the fact that a poll is small, simple and quick. Whereas, a survey can be slightly long, open-ended and time-consuming. A poll allows you to ask one multiple choice question. Participants can choose from among answers that you predefine. You can restrict voters to select just one answer to your question or allow them to choose multiple answers. Surveys are more comprehensive than polls. They usually have a number of questions and are more often than not open-ended.

c. Suppose I wanted to obtain a probability sample of, say, 100 university professors in the Canadian province of Ontario. Using Public sector salary disclosure 2016: all sectors and seconded employees, I find that there are approximately 12,127 people of this rank. Having numbered the list, using some means I would make a random choice of 100 numbers from 1 through 12,127, and then select the names from the list with these numbers. This would be a probability sample. Notice mainly that all members of the list have an equal chance of being selected.
Alternatively I could obtain a non-probability sample of size 100. Suppose I lived in Toronto, near the University of Toronto. Then one way of collecting a convenience sample would be to simply visit one or more Toronto campuses and then visit the offices of a sufficient number of faculty members. Notice now that only Toronto academics have any chance at all of being selected into the sample. Furthermore, if I happen to visit buildings that house mainly science faculty members first then they will dominate the sample. In short, not all Ontario university faculty have an equal chance of being selected in a non-probability sample.

d. Source of errors in survey:
.Sampling Error
Sampling error measures the reliability of a survey and occurs when a random sample of the population of interest is taken. Random sampling means that every member of the population has a known probability of selection, a condition that allows us to make inferences to all of the population within a certain confidence interval. When you hear that the President’s approval rating is 49% with a margin of error of plus or minus 3%, the margin of error provides the measure of reliability, or confidence, in the estimate.

Non-Response Error

Non-response error affects a survey’s accuracy and can occur because members of the sampled population choose not to participate in the survey, are not be able to participate, or choose not to answer a particular question. In a survey of physicians, some may not respond because a gatekeeper doesn’t allow it, some may not respond because they are busy with patients, and some may not respond because they are away from the office.

Coverage Error

Coverage error can also affect accuracy and mainly associated with the sampling frame (the device used to select the sample, such as areas of land, lists of telephone numbers, or lists of addresses) and occurs when units are missing, units not in the population of interest are included, or units are duplicated.

Measurement Error

Measurement error occurs at the intersection of the responder, the interviewer (if used), the questionnaire, and further along in the survey process at data capture and editing. It is the difference between the survey’s measured value of a characteristic and its true value.

Note: We are legally bounded to solve only 4 parts of the problem.
Thank you.