Manufacturing and Product Development

A piston in a particular 12-cylinder diesel engine is manufactured to have diameter 13 mm. Any larger or smaller diameter will cause immediate, costly damage to the engine. Every half-hour, 10 finished pistons are selected and the diameter of each (in mm) is carefully measured. If there is any evidence that the mean diameter is different from 13 mm, the manufacturing process is stopped and the machinery inspected. The quality control inspector uses a significance level of a = 0.05.

a. Suppose the sample mean is x^‾ = 12.89 and the sample standard deviation is s = 0.96. Should the manufacturing process be stopped?

b. Suppose the sample mean is x^‾ = 13.04 and the sample standard deviation is s = 0.045. Should the manufacturing process be stopped?

c. If you were buying these pistons, would you like the manufacturer to use a smaller or a larger significance level? Justify your answer.