Statistics Homework: Sampling Techniques and Questionnaire Design

This document presents a solution to a statistics assignment focusing on sampling techniques. The assignment begins with identifying the target population, which is the business school students, and explains the rationale for using a sample instead of studying the entire population, highlighting time and cost efficiency. The solution then selects stratified random sampling as the most appropriate method, justifying its ability to represent the whole population and minimize bias. A step-by-step breakdown of implementing this technique is provided, including identifying the population, stratification, creating a population list, determining sample size, and assigning sampling fractions. Finally, the document includes a questionnaire with five questions designed to gather relevant information from the selected sample, covering aspects such as the respondent's gender, year of study, support for a new business major, perceived impact of the new major, and potential challenges during its introduction. The assignment is well-structured and provides a clear understanding of the sampling process.

Running head: INTRODUTION TO STATISTICS
1
Sampling Techniques
Student’s Name
Institutional Affiliation

INTRODUCTION TO STATISTICS 2
I have selected Case Study 1.
a. Who or what would be the precise target population? In a couple of sentences, explain
why you have to study a sample of the population.
The target population will be the business school students in the college because the
business major being introduced will be for them.
A sample is best fit study since it consumes less time than studying the population
since assessing all the business students within the given time frame may be
impossible and it is easier to gather data and make inference with a sample rather than
the population (Andrews, L. C., & Phillips, R. L. (2005)). A sample is also more
precise because you have to deal with a smaller number which produces less error
compared to the population. Collecting data from the entire business fraternity may
prove to be more costly than collecting from a portion of them.
b. Based on the case you picked, choose one sampling method to gather data from the
four methods listed below. Explain the rationale behind your selected method.
I would select stratified random sampling since it represents the whole population of
interest. It minimizes bias in sample selection and ensures that each and every
individual of the fraternity is given an equal chance (Brus, D. J., & De Gruijter, J. J.
(1997)). Stratified random sampling also minimizes error compared to other sampling
techniques given the same population.
c. Explain the step-by-step details about how you are going to put this sampling
technique into action.
Step one
Identify the population of interest. In our case our target population is the business
students in the college.
Step two

INTRODUCTION TO STATISTICS 3
Come up with the most suitable stratification. Since we are interested on the views of
the business students on the introduction of major in Real Estate we shall subdivide
the students according to their respective year groups which will now form the basis
of our strata.
Step three
Come up with a list of the population. We should be able to identify all the students in
the college taking business courses. This may be achieved by accessing their records
as it would provide relevant information on the total of these students.
Step four
Come up with a list of the population from the chosen strata. We can now assign a
number say 1 to N to each student in each stratum. From this we will end up with a
list of the respective year groups.
Step five
Identify your sample size. The time and budget allocated for this research can be an
essential tool in determining the sample size usually denoted by n. A sample size can
also be determined using a sample size calculation.
Step six
Assign each stratum an equal sampling fraction. The sample size in each stratum
should be proportionate to population (Onwuegbuzie, A. J., & Leech, N. L. (2007)).
For example, if each of our stratum contains 90, 120, 60 and 120 respectively. We can
take a sampling fraction of ⅓ from each stratum to get a final sample size of 30, 40,
20 and 40 respectively.
Step seven
As we have our sample size we can use either simple random or systematic sampling
to come up with a sample.

INTRODUCTION TO STATISTICS 4
d. Prepare a questionnaire of 5 questions that you would use to acquire necessary
information from the sample you selected.
Questionnaire
1) Sex of the respondent
 Male
 Female
2) The respondent’s current year of study
3) Would you support the introduction of business major in Real Estate in your
school?
 Yes
 No
4) Which impact do you think Real Estate will bring to your college?
5) What are the challenges likely to be encountered during its introduction?

INTRODUCTION TO STATISTICS 5
References
Andrews, L. C., & Phillips, R. L. (2005). Laser beam propagation through random
media (Vol. 152). Bellingham, WA: SPIE press.
Brus, D. J., & De Gruijter, J. J. (1997). Random sampling or geostatistical modelling?
Choosing between design-based and model-based sampling strategies for soil (with
discussion). Geoderma, 80(1-2), 1-44.
Teddlie, C., & Yu, F. (2007). Mixed methods sampling: A typology with examples. Journal
of mixed methods research, 1(1), 77-100.
Gureje, O., Von Korff, M., Simon, G. E., & Gater, R. (1998). Persistent pain and well-being:
a World Health Organization study in primary care. Jama, 280(2), 147-151.
Onwuegbuzie, A. J., & Leech, N. L. (2007). A call for qualitative power analyses. Quality &
Quantity, 41(1), 105-121.
Minasny, B., & McBratney, A. B. (2006). A conditioned Latin hypercube method for
sampling in the presence of ancillary information. Computers & geosciences, 32(9),
1378-1388.