The consulting firm of Winston & Associates has been retained by an electronic component assembly company in Phoenix to design and program a computer simulation model of its operations. Winston & Associates plan to construct the model using ProModel software (see www.Promodel.com). This software allows the developer to program into the model probability distributions for things like machine downtime, defect rates, daily demand, and so forth. The closer the distributions specified in the computer model match those that actually occur in the assembly plant, the better the simulation model will perform. For one machine center, Winston consultants have assumed that when the center goes down for repairs, the time that it will be down will be normally distributed with an average of 30 minutes and a standard deviation equal to 10 minutes. Before finalizing the model, the consultants will collect a random sample of downtimes and test whether their downtime assumptions are valid. The following sample data reflect 10 randomly selected downtimes at this machine center from records over the past four weeks:

a. Using α = 0.05, conduct the appropriate test for the mean downtime at this machine center.
b. Using α = 0.05, conduct the appropriate test for the standard deviation in downtime.
c. Based on the hypothesis tests in parts a and b, what conclusions should the consulting company reach? Discuss.