Philips Semiconductors is a leading European manufacturer of integrated circuits. Integrated circuits are produced on silicon wafers, which are ground to target thickness early in the production process. The wafers are positioned in different locations on a grinder and kept in place using vacuum decompression. One of the goals of process improvement is to reduce the variability in the thickness of the wafers in different positions and in different batches. Data were collected from a sample of 30 batches. In each batch, the thickness of the wafers on positions 1 and 2 (outer circle), 18 and 19 (middle circle), and 28 (inner circle) was measured and stored in Circuits. At the 0.01 level of significance, completely analyze the data to determine whether there is evidence of a difference in the mean thickness of the wafers for the five positions and, if so, which of the positions are different. What can you conclude?
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