A half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml.

(a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?

(b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance.

(c) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hypothesis that the true mean is 520 ml?