The machine that fills bottles is fairly precise. The distribution of the number of ounces of water in the bottles is normal with a standard deviation of 0.06 ounces. The mean is supposed to be 16 ounces, but the machine slips away from that occasionally and has to be readjusted. The water bottling company take a random sample of 10 bottles from today's production and weigh the water in each. The weights are, 15.91, 16.08,16.08,15.94,15.96,16.03,15.82,15.96.
Should the water bottling company readjust the machine? Use a statistical argument to support your advice and include the null and alternative hypothesis. What is the p value and what level of significance is this test statistically significant?