Power of the monitoring procedure

The producer of grit for industrial sandblasting equipment states that their product has a mean particle diameter of 0.76 mm with a standard deviation of 0.08 mm. The quality control department monitors the particle diameter to ensure that the production machines are properly calibrated. If the mean particle size drifts by more than 0.04 mm, the company stops production to recalibrate. A quality control engineer suggests that they sample 20 particles each day to determine whether the system still meets specifications. The quality control team currently uses the .05 significance level for their tests.

(a) The vice president of sales is concerned that the power for the proposed procedure is too low. What sample size would the quality control team need to achieve 90 percent power?

(b) The risk management team is concerned that unnecessary recalibrations will be too expensive for the company. How could the quality control team reduce the risk of unnecessary recalibrations? Explain how the change would affect the power of the monitoring procedure.

(c) The CEO wants to increase quality standards to ensure the mean diameter is no more than 0.02 mm from the stated specifications. Explain how the change would affect the power of the monitoring procedure