As the number of degrees of freedom for the t-distribution increases, the difference between the t-distribution and the standard normal distribution becomes smaller. This convergence is a consequence of the Central Limit Theorem, where the t-distribution approaches the standard normal distribution with increasing degrees of freedom.
Option B is correct.
As the number of degrees of freedom for the t-distribution increases, the difference between the t-distribution and the standard normal distribution becomes smaller. The t-distribution approaches the standard normal distribution as the degrees of freedom increase, and in the limit, they become equivalent.
The t-distribution is a family of distributions that is symmetric and bell-shaped, similar to the standard normal distribution. However, its variability depends on the degrees of freedom. When the degrees of freedom are low, the tails of the t-distribution are fatter compared to the standard normal distribution. As the degrees of freedom increase, the t-distribution becomes more concentrated around the mean, and the shape of the distribution approaches that of the standard normal distribution.
In essence, with an increasing number of degrees of freedom, the t-distribution converges to the standard normal distribution. This convergence is a result of the Central Limit Theorem, which states that the distribution of the sum (or average) of a large number of independent, identically distributed random variables approaches a normal distribution, regardless of the shape of the original distribution.
In conclusion, the correct answer is:
B. becomes smaller