Determine the approximate sample size needed for a paired comparison ????-test when

(a) ????0 ∶ ???????? = ????????, ???? = 2.4, ???? = 0.05, ???? = 0.05, and ????̇ = 10.

(b) ????0 ∶ ???????? = ????????, ???? = 20, ???? = 0.05, ???? = 0.10, and ????̇ = 50.

(c) ????0 ∶ ???????? ≤ ????????, ???? = 1.2, ???? = 0.05, ???? = 0.15, and ????̇ = 6.

(d) ????0 ∶ ???????? ≥ ????????, ???? = 200, ???? = 0.01, ???? = 0.10, and ????̇ = 750.

(e) ????0 ∶ ???????? ≤ ????????, ???? = 20, ???? = 0.05, ???? = 0.05, and ????̇ = 100.