Assuming the normality assumptions are satisfied and ???????? ≈ ????????, determine the rejection region for a two-sample ????-test for comparing the means ???????? and ???????? when

(a) ????0 ∶ ???????? ≤ ????????, ???? = 0.05, ???????? = 30, and ???????? = 25.

(b) ????0 ∶ ???????? ≥ ????????, ???? = 0.05, ???????? = 50, and ???????? = 75.

(c) ????0 ∶ ???????? ≤ ????????, ???? = 0.01, ???????? = 60, and ???????? = 60.

(d) ????0 ∶ ???????? = ????????, ???? = 0.05, ???????? = 120, and ???????? = 150.