#### 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

#### Included in

Applied Statistics Commons, Social and Behavioral Sciences Commons, Statistical Theory Commons