life An engineering experiment called for running three factors; Pressure (factor A), Table speed (factor B) and Down force (factor C), each at a 'high' and 'low' setting, on a production tool to determine which had the greatest effect on product uniformity. Two replications were run at each setting. The results from the experiments are summarised in the table below. Test (1) A B AB C AC BC ABC Observation -3, -1 0, -1 -1, 0 +2, +3 -1, 0 +2, +1 +1, +1 +6, +5 (a) Calculate and comment on the estimate of the AC interaction effect. [8 marks] (b) Explain the difference, in interpretation, between a negative and positive AC inter- action effect. [4 marks] (c) Determine an estimate of the error variance. [4 marks] (d) What is the null and alternative hypotheses when testing the significance of the AC interaction effect? [2 marks] (e) Using 5% level of significance, test the claim that there is no interaction between Pressure (A) and Down force (C) in product uniformity. State the conclusion of the test in context. [8 marks] (f) Plot the AC interaction effect. [4 marks]