Assuming a random sample has been selected from a population that is approximately normally distributed, use a ????-test to perform each of the following hypothesis tests. In particular, include the rejection region, the value of ????obs, the decision concerning ????0, and the approximate ????-value associated with ????obs.

(a) Test ????0 ∶ ???? = 100 when ???? = 0.05, ???? = 30, ????̄ = 95.5, and ???? = 7.6.

(b) Test ????0 ∶ ???? ≤ 5 when ???? = 0.01, ???? = 50, ????̄ = 6.5, and ???? = 3.9.

(c) Test ????0 ∶ ???? ≥ 60 when ???? = 0.05, ???? = 61, ????̄ = 58.5, and ???? = 4.5.

(d) Test ????0 ∶ ???? ≤ 1000 when ???? = 0.01, ???? = 121, ????̄ = 1095.1, and ???? = 223.9.