Plastic fill process. University of Louisville researchers J. Usher, S. Alexander, and D. Duggins examined the process of filling plastic pouches of dry blended biscuit mix (Quality Engineering, Vol. 91, 1996). The current fill mean of the process is set at µ = 406 grams, and the process fill standard deviation is σ = 10.1 grams. (According to the researchers, "The high level of variation is due to the fact that the product has poor flow properties and is, therefore, difficult to fill consistently from pouch to pouch.") Operators monitor the process by randomly sampling 36 pouches each day and measuring the amount of biscuit mix in each. Consider , the mean fill amount of the sample of 36 products. Suppose that on one particular day, the operators observe  = 400.8. One of the operators believes that this indicates that the true process fill mean LL for that day is less than 406 grams. Another operate argues that µ = 406, and the small value of  observed is due to random variation in the fill process. Which operator do you agree with? Why?