In English texts, the choice between a capital "N" and a lowercase "n" depends on whether you are referring to the total population or a specific subgroup. Here is the standard rule used in scientific and statistical writing (such as APA style):
Use lowercase "n" when referring to a subsample or a specific group within a larger study. For example, if a study looked at 100 people total, but only 45 were men, you would write: "The male subgroup (n = 45) showed significant improvement".
Use uppercase "N" when referring to the total population or the entire sample size of a study. For example: "The total sample size for the study was N = 100".
"Weekly Language Usage Tips: n or N in sample sizes ..." Language Usage Weblog February 23, 2012.
