In any canning process, a manufacturer will lose money if the cans contain either significantly more or significantly less than is claimed on the label. Accordingly, canners pay close attention to the amount of their product being dispensed by the can-filing machines. Consider a company that produces a fast-drying rubber cement in 32-ounce aluminum cans. A quality control inspector is interested in testing whether the variance of the amount of rubber cement dispensed into the cans is more than .3. If so, the dispensing machine is in need of adjustment. Since the inspection of the canning process requires that the dispensing machines be shut down, the shutdowns for an lengthy period of time cost the company thousands of dollars in lost revenue, the inspector is able to obtain a random sample of only 10 cans for testing. After measuring the weights of their contents, the inspector computers that the sample mean is 31.55 ounces and the sample standard deviation is 0.48 ounce. Required:
a. Does the sample evidence indicate that the dispensing machines are in need of adjustment? Test at significance level α= 0.05.
b. What assumption is necessary for the hypothesis test of part a to be valid?