Use this diagram to demonstrate that the t- test statistic has greater spread than the standard normal distribution, especially when the sample size is small.
- Click Accumulate then take about 50 random samples of n = 20.
The distribution of t statistic conforms reasonably with a standard normal distribution.
- Reduce the sample size to n = 5 and take 100 more samples.
Values of t less than -3 or more than +3 occur more often than expected
from a standard normal distribution.
- Reduce the sample size to n = 3 and repeat. It should be
clear that t has greater spread than a standard normal distribution.
- Click on the crosses for the most extreme t-values. They usually arise when
the 3 sample values are close together and s is small.