A gage repeatability experiment was performed by Lexon Corporation using three instruments to measure parts set to diameter of 20 mm. It was thought that operator differences might affect the outcomes. Each of three operators used three of the same type of instrument to make four determinations of the diameters of a part, leading to a nested design. The responses are as follows:

Analyze the data and test for significance of operator and instrument at 5% level of significance.

Operator I 11: 20.5 20.2 20.3 20.4 12: 21.0 20.7 20.8 21.1 13: 20.1 20.9 20.6 20.7 II 14: 20.7 20.8 20.8 20.4 15: 21.2 21.3 20.8 20.6 16: 20.8 21.3 21.4 21.4 III 17: 20.8 20.9 21.0 20.9 18: 20.6 20.5 20.2 20.3 19: 21.4 21.5 20.7 21.3