1.The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. The Rockwell hardness of a particular alloy is 70. A new annealing process is implemented with the goal of increasing the Rockwell hardness of the alloy. A test of 50 samples with the new annealing process resulted in a sample mean of 72.1 and a sample standard deviation of 5.

a)Does the sample data indicate that the true average Rockwell hardness should be greater than 70 at a significance level of 0.01?

b)If the true average Rockwell hardness is 72, what is the probability of committing a type 2 error using the test in part a?

c)What is the value of n needed to satisfy =0.01 and (72)=0.01?