Determine the common sample size (i.e., ???????? = ????????) for a two-sample ????-test when

???????? ≈ ???????? and

(a) ????̇ = 20, ???? = 5, ???? = 0.05, and ???? = 0.10 for an upper-tail test.

(b) ????̇ = 40, ???? = 5, ???? = 0.05, and ???? = 0.05 for a lower-tail test.

(c) ????̇ = 20, ???? = 10, ???? = 0.01, and ???? = 0.10 for an upper-tail test.

(d) ????̇ = 250, ???? = 80, ???? = 0.05, and ???? = 0.05 for a two-tail test.

(e) ????̇ = 25, ???? = 2.5, ???? = 0.05, and ???? = 0.15 for an lower-tail test.

(f) ????̇ = 50, ???? = 15, ???? = 0.01, and ???? = 0.10 for an two-tail test.