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From $n_1$ p-dimensional random vectors: $X_1,...,X_{n_1}$ independents with $X_i\sim N_p(\mu_1,\Sigma)$ and $n_2$ random vectors with the same dimension: $Y_1,...,Y_{n_2}$ independents with $Y_i\sim N_p(\mu_2,\Sigma)$. Find a statistic wich estimate the difference between population means and wich has $T^2$ Hotelling distribution.

I really stuck on this problem in the way I don't know how to create this statistic.

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