Consider the results of the group stage matches from two FIFA World Cups, namely the $2002$ tournament in Japan/South Korea and the 2018 tournament in Russia (N = 96). Let $X_1$ be the number of goals scored in the first half, $X_2$ be the number of goals scored in the second half, and $D = X_2 - X_1$. We have: $X_1 = 1.03$, $SA₁ = 1.11$, $X_2 = 1.58$, $SA_2 = 1.04$, $D = 0.55$, $SA_D = 1.44$.
This was originally a multiple choice question.
One of the given answers was the standard error of $D$ is $\sqrt{1.11^2/96+1.04^2/96}$ which i believed to be the correct solution, which unfortunately wasn't.
But this is also the formula i was given when calculating the standard error for differences of variables. Can someone tell me why this is wrong?