A process engineer has been assigned to investigate if there is an increase in productivity by improving the quality spec of a particular raw material used in production. The data analysis consisted of 6 randomly selected days in which production achieved contained the LOW quality raw material compared to 6 randomly selected days in which production achieved contained the HIGH quality raw material. The unit production times in seconds are given below. Time to Produce One Unit (in seconds) Day LOW Quality HIGH Quality 1 17 17 2 21 18 3 18 16 4 24 23 5 17 18 6 15 14 1) Two-Sample T-Test and CI: LOW Quality, HIGH Quality Two-sample T for LOW Quality vs HIGH Quality N Mean StDev SE Mean LOW Quality 6 18.67 3.27 1.3 HIGH Quality 6 17.67 3.01 1.2 Difference = mu (LOW Quality) - mu (HIGH Quality) Estimate for difference: 1.00000 90% upper bound for difference: 3.48850 T-Test of difference = 0 (vs >): T-Value = 0.55 P-Value = 0.703 DF = 10 Both use Pooled StDev = 3.1411 2) Two-Sample T-Test and CI: LOW Quality, HIGH Quality Two-sample T for LOW Quality vs HIGH Quality N Mean StDev SE Mean LOW Quality 6 18.67 3.27 1.3 HIGH Quality 6 17.67 3.01 1.2 Difference = mu (LOW Quality) - mu (HIGH Quality) Estimate for difference: 1.00000 90% CI for difference: (-2.32440, 4.32440) T-Test of difference = 0 (vs not =): T-Value = 0.55 P-Value = 0.595 DF = 9 3) Paired T-Test and CI: LOW Quality, HIGH Quality Paired T for LOW Quality - HIGH Quality N Mean StDev SE Mean LOW Quality 6 18.6667 3.2660 1.3333 HIGH Quality 6 17.6667 3.0111 1.2293 Difference 6 1.00000 1.41421 0.57735 90% CI for mean difference: (-0.16339, 2.16339) T-Test of mean difference = 0 (vs not = 0): T-Value = 1.73 P-Value = 0.144

(4) a) Assume the times are normally distributed. Which Minitab output you should use to determine if there is a significant difference in production time between LOW and HIGH quality raw material spec? Include the reasons you choose the particular output. (6) b) Is there a significant difference in production time between the LOW and the HIGH quality raw material spec? Perform a full hypothesis test at the 10% level of significance and using the output you choose in part a).