A packaging company that bottles soda in 12 oz. bottles is interested in monitoring the machines to ensure quality control. Over the years, it has been determined that the machines has a natural standard deviation of 0.49 oz. and the distribution of volumes is normally distributed. A quality control manager takes a random sample of 40 sodas with a sample mean of 12.3 oz. At the 5% level of significance, test the following hypotheses:
1) Perform a one-tail hypothesis, testing the claim that the true mean is 12 as opposed to the machine overfilling the bottles
2) Perform a two-tail hypothesis, testing the claim that the true mean is 12 versus the alternative that the machine is off, either way