Why the significance level of large values of " n " is sensitive. - Compare: n=1 to n > 3000
1) The Variance formula - composed of " a " , " b " , and " n " which their calculated value equals the Variance.
2) " b " is the upper limit , while " a " is the lower limit and varies up to " b " the upper limit.
3) " n " is a limiting factor: small values of " n " have a large range which is set by " b "
4) If " n " is very large - the range of " b " is very limited and any change from that range will be noticed
5) Set " b " - move " a " to observe range
6) reset " b " and move " a " to see the new observed range
7) adjust " n " and see how it impacts both " a " and " b "

This is the standard variance formula with a visual as to how it works