According to the law of large numbers the larger the sample size (n), the more likely it is that the sample mean is close to the population mean. The same principle holds true for sample variance and the t statistic: For t statistics, however, this relationship is typically expressed in terms of the degrees of freedom, or the df value for the sample variance instead of sample size (n): As sample size increases, so does the value for degrees of freedom, and will be a better estimate of σ. Thus, the value for degrees of freedom associated with also describes how well t estimates z.
