If $X_i$ and $Y_j$ are normal distributions where $i = 1,...,n$ and $j= 1,...,n$ with different $\mu$ but same $\sigma^2$, and $\mu_x$ - $\mu_y$ = $\sigma/3$ what is common sample size $n$ needed to be 95% certain of correctly selecting group with higher mean?
What means common sample size? What test we use (t or Z?) to get 95% confidence?