Question

Explain why the​ t-distribution has less spread as the number of degrees of freedom increases.

Answer 1

The explanation is below;

Explanation:

Spread in t-distribution decreases as sample size increases. As sample size increases, the t-distribution behaves more like standard normal distribution (the density curve of t-distribution gets closer to the standard normal density curve). As degrees of freedom increases, spread of t-distribution decreases because sample size increases sampling distribution of standard deviation becomes closer to sigma (population standard deviation) by the law of large numbers