A manufacturer makes silicon strain gauge transducers that are designed to produce a linear voltage output that is directly proportional to the applied pressure. Six different processing lines are used to manufacture the gauges.

In this application an important physical property of the silicon layer formed to fabricate the gauge is its Young's modulus. There have been some calibration problems with the gauges and an engineer suspects that one of the process lines is producing a mean value of Young's modulus that is different from that of the other processing lines.

The Young's modulus of the silicon was measured from a random sample of four gauges taken from each of the processing lines. The results [in GPa] are given in the table below.

Your manager asks you to test the engineer's hypothesis by performing an analysis of variance at the 0.05 level of significance. He has, moreover, heard about 'Six Sigma' and asks you to advise if its introduction would alleviate any supposed issues with the manufacturing of the gauges.

Produce a short report to update your manager on both the method and results of your analysis and the introduction od 'Six Sigma'.