Home > OA_JOURNALS > JMASM > Vol. 15 (2016) > Iss. 2

#### Article Title

#### Abstract

When the sample size *n* is small, the random variable T= √n(\overline{X} – *μ)/S* is said to follow a central *t* distribution with degrees of freedom (*n* – 1), where \overline{X} is the sample mean and *S* is the sample standard deviation, provided that the data *X* ~ *N* (*μ*, *σ*^{2}). The random variable *T* can be used as a test statistic to hypothesize the population mean *μ*. Some argue that the *t*-test statistic is robust against the normality of the distribution and claim that the normality assumption is not necessary. In this article we will use simulation to study whether the *t*-test is really robust if the population distribution is not normally distributed. In particular, we will study how the skewness of a probability distribution will affect the confidence interval as well as the *t*-test statistic.

#### DOI

10.22237/jmasm/1478001960

#### Recommended Citation

Lim, Wooi K. and Lim, Alice W.
(2016)
"A Comparison Of Usual t-Test Statistic and Modified t-Test Statistics on Skewed Distribution Functions,"
*Journal of Modern Applied Statistical Methods*: Vol. 15
:
Iss.
2
, Article 8.

DOI: 10.22237/jmasm/1478001960

Available at:
http://digitalcommons.wayne.edu/jmasm/vol15/iss2/8