In: Statistics and Probability
An engineer analyzes a production process with the goal of reducing both production mean time and variability and develops and implements a solution. 30 observations are collected before the solution is implemented (with X ̅= 45.3 minutes and S=5.2 minutes), and then an additional 40 observations collected after implementation (with X ̅= 41.3 minutes and S=3.2 minutes). Historically, σ=5.4 minutes for the process. Does it appear that the engineer has in fact reduced the average production time? Or is the lower sample mean just a matter of chance? Assume the variance is unknown and unequal. Include supporting calculations and explanation to support your conclusion. Does it appear that the engineer has in fact reduced the variability of the process? Include supporting calculations and explanation to support your conclusion