In: Statistics and Probability
The Rockwell hardness of a metal is determined by impressing a
hardened point into the surface...
- 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.
- Does the sample data indicate that the true average Rockwell
hardness should be greater than 70 at a significance level of
0.01?
- If the true average Rockwell hardness is 72, what is the
probability of committing a type 2 error using the test in part
a?
- What is the value of n needed to satisfy α=0.01 and
β(72)=0.01?