A preliminary experiment is conducted to study the effects of four factors and their interactions on the output of a certain machining operation. Two runs are made at each of the treatment combinations in order to supply a measure of pure experimental error. Two levels of each factor are used, resulting in the data shown here. Make tests on all main effects and interactions at the 0.05 level of significance. Drawconclusions.

Treatment Combination Replicate 1 Replicate 2 7.9 (), 9.6 9.1 8.6 10.4 7.1 11.1 16.4 10.2 5.8 12.0 8.3 12.3 15.5 8.7 15.2 5.8 ab ac ad be 7.1 12.6 bd cd abc abd 4.7 7.4 21.9 9.8 10.9 21.9 7.8 acd bed abcd 13.8 11.2 10.2 12.8 11.1 14.3