2.t distribution is a cluster of curves, and its morphological changes are related to the size of n (exactly, to the degree of freedom ν). The smaller the degree of freedom ν, the lower and flatter the T distribution curve; The greater the degree of freedom v, the closer the T distribution curve is to the standard normal distribution (U distribution) curve, as shown in the figure.
T(n) distribution and density function of standard normal N(0, 1)
For each degree of freedom ν, there is a t distribution curve, and there is a distribution law of statistics t under each curve, so the calculation is more complicated.
T distribution of students (or T distribution) plays an important role in probability statistics, confidence interval estimation and significance test calculation.
The overall standard deviation of t distribution (which is true in almost all practical statistical work) is unknown and should be estimated according to the data. Deal with the standard deviation of textbook problems, because if we call it two categories: (1) those differences estimated on the basis of manageable data with such a large sample size seem to be certain; (2) These examples illustrate mathematical reasoning, in which the estimated standard deviation is not considered for the time being, because it is not a point, which was explained by the author or tutor at that time.