[size=100]One hundred samples are drawn from a normal population with [math]\mu[/math]= 100 and [math]\sigma[/math] = 5. [br]For each sample a test statistic is calculated in two ways, either using the population standard deviation or the sample standard deviation.[br][br]When sample size is small, the sample standard deviation varies much more than when sample size is large. This often leads to extreme test statistics ("fat tails") for small samples. [/size]