Final answer:
In statistics, as the sample size N increases, the critical value of t in a t-distribution gets smaller because the distribution becomes more like the standard normal distribution.
Step-by-step explanation:
The question is concerning the relationship between the sample size (N) and the critical value of t in a t-distribution, which is used in statistics.
As sample size N gets larger, the t-distribution approaches a normal distribution and the critical value of t gets smaller. This is because, with a larger sample size, there is less variability and the t-distribution becomes more like the standard normal distribution, which has fixed critical values that do not change with sample size.