In a certain industrial process, an automatic grinding machine that produces the least surface roughness is to be selected. Four repeat test were run, using machines submitted by three different suppliers and the following data were obtained. Determine with 95% confidence whether there is any significant difference between machines, and if so which one should be selected.

Method Null hypothesis All means are equal Alternative hypothesis Not all means are equal Significance level 0 = 0.05 Equal variances were assumed for the analysis. Factor Information Factor Levels Values Factor 3 ABCAnalysis of Variance Source DF Adj SS Adj MS F-Value P-Value Factor 2 105.50 52.750 37.24 0.000 Error 9 12.75 1.417 Total 11 118.25 Model Summary S R-sq R-sq(adj) R-sq(pred) 1.19024 89.22% 86.82% 80.83% Means Factor N Mean StDev 95% CI A 4 20.000 1.155 (18.654, 21.346) B 4 12.750 0.957 (11.404, 14.096) 4 16.000 1.414 (14.654, 17.346) Pooled 5tDev = 1.19024