Integrated circuits consist of

Integrated circuits consist of electric channels that are etched onto silicon wafers.

 A certain proportion of circuits are defective because of “undercutting,” which occurs when too much material is etched away so that the channels, which consist of the unetched portions of the wafers, are too narrow. A redesigned process, involving lower pressure in the etching chamber, is being investigated. The goal is to reduce the rate of undercutting to less than 5%. Out of the first 100 circuits manufactured by the new process, only 4 show evidence of undercutting. True or false: a. Since only 4% of the 100 circuits had undercutting, we can conclude that the goal has been reached.

b. Although the sample percentage is under 5%, this may represent sampling variation, so the goal may not yet be reached.

 c. There is no use in testing the new process, because no matter what the result is, it could just be due to sampling variation.

 d. If we sample a large enough number of circuits, and if the percentage of defective circuits is far enough below 5%, then it is reasonable to conclude that the goal has been reached.

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