Manufacturing. A wire manufacturer produces copper wires of an average diameter of 0.72 mm. The manufacturer is wondering whether the wire would have the same diameter under a new manufacturing method. For a sample of 20 wires, it was determined that the average diameter is 0.68 mm with a standard deviation of 0.2 mm. The 90%

confidence interval estimate for this sample is 0.60 mm to 0.76 mm.

a) What is the margin of error for this problem?

b) The manufacturer commented that the interval was too wide. Explain specifically what should be done to reduce the margin of error to no more than {0.05 mm.