ISSN Print: 2381-1218  ISSN Online: 2381-1226
Computational and Applied Mathematics Journal  
Manuscript Information
 
 
Sample Size and Its Role in Central Limit Theorem (CLT)
Computational and Applied Mathematics Journal
Vol.4 , No. 1, Publication Date: Feb. 27, 2018, Page: 1-7
767 Views Since February 27, 2018, 1099 Downloads Since Feb. 27, 2018
 
 
Authors
 
[1]    

Mohammad Rafiqul Islam, Department of Mathematics and Natural Sciences (MNS), BRAC University, Dhaka, Bangladesh.

 
Abstract
 

It is very important to determine the proper or accurate sample size in any field of research. Sometimes researchers cannot take the decision that how many number of individuals or objects will they select for their study purpose. Also, a set of survey data is used to verify that central limit theorem (CLT) for different sample sizes. From the data of 1348 students we got the average weight for our population of BRAC University students is 62.62 kg with standard deviation 11.79 kg. We observed that our sample means became better estimators of true population mean. In addition, the shape of the distribution became more Normal as the sample size increased. So it is concluded that our simulation results were consistent with central limit theorem.


Keywords
 

Sample Size, Inference, Precision, Confidence Interval (CI), Population and Sample


Reference
 
[01]    

A. I. Fleishman, “A Method for Simulating Non-Normal Distributions”, Psychometrika, Vol. 43, No. 4, pp. 521-532, 1978. View at Google Scholar.

[02]    

D. R. Cox, “Some Problems Connected with Statistical Inference”, The Annals of Mathematical Statistics, Vol. 29, No. 2 pp. 357-372, Institute of Mathematical Statistics, Jun., 1958. View at Google Scholar.

[03]    

E. H. Holton and M. B. Burnett, Qualitative research methods, In R. A. Swanson, & E. F. Holton (Eds.), Human resource development research handbook: Linking research and practice, San Francisco: Berrett-Koehler Publishers, 1997.

[04]    

George Miaoulis and R. D. Michener, An Introduction to Sampling. Dubuque, Iowa: Kendall/Hunt Publishing Company, 1976.

[05]    

Glenn D. Israel, “Sampling: The Evidence of Extension Program Impact”, Program Evaluation and Organizational Development, IFAS, University of Florida, PEOD-5, 1992. View at Google Scholar.

[06]    

Glenn D. Israel, “Determining Sample Size”, Program Evaluation and Organizational Development, Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida, PEOD-6, November 1992. View at Google Scholar.

[07]    

H. Arsham, System Simulation: The Shortest Route to Applications, Version 9, 2005, Retrieved 1/1/20176 from http://home.ubalt.edu/ntsbarsh/simulation/sim.htm.

[08]    

I. Peers, Statistical analysis for education and psychology researchers, PA: Falmer Press, Bristol, 1996. View at Google Scholar.

[09]    

H. Watt James and van den Berg Sjef, Research Methods for Communication Science, Part II: Basic Tools of Research: Sampling, Measurement, Distributions, and Descriptive Statistics, pp. 136-137, Allyn & Bacon, Inc, 2002.

[10]    

James E. Barlett, Joe W. Kotrlik and Chadwick C. Higgins, “Organizational research: Determining appropriate sample size in survey research”, Information Technology, Learning, and Performance Journal, Vol. 19, No. 1, pp. 43-50, Spring 2001. View at Google Scholar.

[11]    

Joe L. Spaeth, “Perils and pitfalls of survey research”, Applying Research to Practice: Allerton Park Institute Proceedings (no. 33, 1991), Graduate School of Library and Information Science, University of Illinois at Urbana-Champaign, 1992. View at Google Scholar.

[12]    

Leslie Kish, Survey Sampling, John. Wiley and Sons, Inc., New York, 1965.

[13]    

Martin N. Marshall, “Sampling for qualitative research”, Oxford Journals: Medicine & Health Family Practice, Volume 13, Issue 6, pp. 522-526, 1996. View at Google Scholar.

[14]    

P. O. Johnson, “Development of the sample survey as a scientific methodology”, Journal of Experiential Education, Taylor & Francis, Ltd., vol. 27, no. 3, pp. 167-176, March 1959. View at Google Scholar.

[15]    

R. C. Geary, “Testing for normality” Biometrika, vol. 34, pp. 209-242, 1947.

[16]    

R. V. Krejcie and D. W. Morgan, “Determining sample size for research activities”, Educational and Psychological Measurement, pp. 30, pp. 607-610, 1970. View at Google Scholar.

[17]    

S. Sudman, Applied sampling, Academic Press, New York, 1976.

[18]    

T. Micceri, “The Unicorn, The Normal Curve, and Other Improbable Creatures”, Psychological Bulletin, 105 (1), pp. 156-166, 1989. View at Google Scholar.

[19]    

Taro Yamane, Statistics, An Introductory Analysis, 2nd Ed., Harper and Row, New York, 1967.

[20]    

W. G. Cochran, Sampling techniques, John Wiley & Sons, 3rd ed., New York, USA, 1977.

[21]    

W. L. Hays, Statistics, 5th ed., New York: Holt, Rinehart and Winston, 1994.





 
  Join Us
 
  Join as Reviewer
 
  Join Editorial Board
 
share:
 
 
Submission
 
 
Membership