# why sample size has been included in the variance difference formula ?

Hello 365 Team,

At 2.55 Minute, we have been provided with variance of the difference formula, where why the formula has included sample size in the denominator.

Exact detailed solution from your end, will help us understand things better

Thanks

1 answers ( 0 marked as helpful)

When two independent random variables are combined, the variances of these variables add up. This property allows us to combine the variances of the two sample means. so if mean(x1 - x2) = mean(x1) - mean(x2), then var(x1 - x2) is actually Var(x1) + Var(x2).

We are actually calculating the sample error of the sample mean in each (var_pop / n) instead (var_sam / n-1), then using above fact to take the magnitudeof the 2 standard errors.