As the degrees of freedom increase, the dispersion of the t distribution:

As the degrees of freedom increase, the dispersion of the t distribution decreases. This is because the shape of the t distribution becomes closer to the standard normal distribution (z distribution) as the degrees of freedom grow. With fewer degrees of freedom, the t distribution has heavier tails, indicating more variability and potential for extreme values. However, as the degrees of freedom increase, the distribution tightens, and the tails become less heavy, leading to a smaller dispersion around the mean.

This behavior is significant in statistical analysis, particularly in hypothesis testing and confidence interval estimation, where larger sample sizes are associated with more reliable results and less uncertainty. Thus, understanding how the dispersion changes with degrees of freedom is crucial for accurately interpreting results in statistics.