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The Rockwell hardness of a metal is determined by impressing a hardened point into the surface...

  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.

  1. Does the sample data indicate that the true average Rockwell hardness should be greater than 70 at a significance level of 0.01?
  2. If the true average Rockwell hardness is 72, what is the probability of committing a type 2 error using the test in part a?
  3. What is the value of n needed to satisfy α=0.01 and β(72)=0.01?

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orchestra answered 2 years ago
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