Share This Article:

On the Distribution of Type II Errors in Hypothesis Testing

Abstract Full-Text HTML Download Download as PDF (Size:732KB) PP. 189-195
DOI: 10.4236/am.2011.22021    4,665 Downloads   8,608 Views   Citations
Author(s)    Leave a comment

ABSTRACT

When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has changed. We consider this issue and quantify matters in a manner that differs a bit from what is commonly done. In particular, we define the probability distribution function for Type II errors. We then explore some interesting properties that we have not seen mentioned elsewhere for this probability distribution function. Finally, we discuss several Maple procedures that can be used to perform various calculations using the distribution.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

S. Thompson, "On the Distribution of Type II Errors in Hypothesis Testing," Applied Mathematics, Vol. 2 No. 2, 2011, pp. 189-195. doi: 10.4236/am.2011.22021.

References

[1] D. C. Montgomery, “Statistical Process Control,” John Wiley & Sons, 1991.
[2] D. S. Wackerly, W. Mendenhall, and R. L. Scheaffer, “Mathematical Statistics with Applications,” Duxbury Press, 1996.
[3] S. Thompson, “Maple Worksheets for Investigating Type II Errors,” 2010. http://www.radford.edu/thompson/TypeIIErrors/index.html
[4] Maplesoft, Waterloo Maple Inc., Waterloo, 2010.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.