Suppose the Cozy Cola company produces cans of cola containing a nominal volume of 355 ml. An government inspector periodically makes unannounced visits to the company to test the claim. By formal agreement, the inspector will base a "compliance decision" upon a statistical significance test. Specifically, here are the hypotheses:
H_0: mu = 355
H_1: mu < 355.
Suppose it is known that the volume of a can is a normal distribution with mean mu (unknown) and known standard deviation 2 ml. The significance text will use a sample size of n=12 and an alpha level of .05. The decision rule will be:
Reject H_0 in favor of H_1 iff X-bar <= x*.
Find x*.
Now, make a decision based upon this sample of volumes, measured on a particular day:
354.3 352.9 357.9 351.6 353.4 354.5 355.3 358.9 356.8 354.9 351.4 354.6 NOTE: The sample mean here is 354.71.Suppose instead, the sample on another day was:
352.4 353.2 353.9 350.1 355.1 356.3 353.2 352.3 352.0 350.4 357.4 354.0 NOTE: Sample mean = 353.36.What is your decision here?