Determine the approximate sample size required for a ????-test about the mean of population when

(a) ????0 ∶ ???? ≤ 25, ????0 − ????crit = 5, ???? = 0.01, ???? = 0.10, and ????̇ = 14.

(b) ????0 ∶ ???? ≥ 90, ????0 − ????crit = 4, ???? = 0.01, ???? = 0.10, and ????̇ = 10.

(c) ????0 ∶ ???? ≥ 500, ????0 − ????crit = 20, ???? = 0.05, ???? = 0.10, and ????̇ = 250.

(d) ????0 ∶ ???? = 1000, ????0 − ????crit = 50, ???? = 0.05, ???? = 0.10, and ????̇ = 120.

(e) ????0 ∶ ???? = 0, ????0 − ????crit = 0.5, ???? = 0.01, ???? = 0.10, and ????̇ = 1.5.