A curing process for cement results in a mean compressive strength of 5000kg per cm^2 with a standard deviation of 120 kg per cm^2. A new curing process is proposed, and a random sample of 50 pieces of cement is tested. To test H0: u = 5000 versus H1: u < 5000 with respect to the new curing process, the critical region X < 4970 is determined.

a) provide the statistical model stating all assumptions

b) what is the probability of committing a Type I error

c) Evaluate the power of the test when u = 4960