Question: As part of the manufacturing process for its personal computers, Empire Electronics electroplates various precious metals onto certain circuitry. The design specifications call for a mean average of 50 micro-inches of each form of metal. If the plating is too thick, the expensive metal is wasted; if it is too thin, the component will fail to operate properly.

(a) The quality inspectors at Empire randomly sampled the thickness of gold electroplated onto 64 Model Alpha circuits, which were found to have a sample mean of 52.106 micro-inches and a sample standard deviation of 6.48 micro-inches. If the maximum permissible Type I Error is 1%, explain whether or not the gold electroplating process for Model Alpha is acceptable, given the available evidence. [COMMENTS & HINTS: Use hypothesis testing, confidence levels, and p-values to justify or explain the conclusion. Clearly state the conclusion, interpreting it within the context of this scenario.]

(b) The quality inspectors at Empire randomly sampled the thickness of silver electroplated onto 81 Model Beta circuits, which were found to have a sample mean of 47.3025 micro-inches and a sample standard deviation of 7.47 micro-inches. If the maximum permissible Type I Error is 0.1%, explain whether or not the silver electroplating process for Model Beta is acceptable, given the available evidence. [COMMENTS & HINTS: Use hypothesis testing, confidence levels, and p-values to justify or explain the conclusion. Clearly state the conclusion, interpreting it within the context of this scenario.]