In each of the following scenarios, determine the rejection region, the value of ????, the value of

In each of the following scenarios, determine the rejection region, the value of ˆ????, the value of ????obs, the ????-value, and the appropriate testing decision for ????0.

(a) ????0 ∶ ???????? ≤ ????????, ???? = 0.05, ???????? = 175, ˆ???????? = 0.39, ???????? = 165, and ˆ???????? = 0.33.

(b) ????0 ∶ ???????? ≥ ????????, ???? = 0.05, ???????? = 150, ˆ???????? = 0.22, ???????? = 142, and ˆ???????? = 0.31.

(c) ????0 ∶ ???????? = ????????, ???? = 0.05, ???????? = 225, ˆ???????? = 0.76, ???????? = 165, and ˆ???????? = 0.65.

(d) ????0 ∶ ???????? ≥ ????????, ???? = 0.05, ???????? = 590, ˆ???????? = 0.42, ???????? = 655, and ˆ???????? = 0.49.

(e) ????0 ∶ ???????? ≤ ????????, ???? = 0.01, ???????? = 980, ˆ???????? = 0.16, ???????? = 1275, and ˆ???????? = 0.11.