Can you reject the null hypothesis of no interactions? Explain.

Exercises 5–7 refer to the following data:
A machine shop has four machines used in precision grinding of bearings. Three machinists are employed to grind bearings on the machines. In an experiment to determine whether there are differences in output among the operators or the machines, each operator worked on each machine for three days. The response variable was the number of parts produced. The results are presented in the following table.

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Machine 1 Machine 2 Operator A 38 33 20 40 43 47 43 31 40 Machine 3 Machine 4 40 38 39 Operator B Operator C 33 34 34 39 37 47 35 43 31 36 46 46 28 34 40 49 36 50 39 37 35 34 39 38