A machine at AMT & Co. fills 120-ounce jugs with laundry softener. A quality control inspector wishes to test if the machine needs an adjustment or not, which is needed when the machine either overfills or underfills the jugs. Assume the distribution of the fill volume in these jugs is normal. Under standard circumstances, the mean amount should be 120 ounces with a standard deviation of 1 ounce. A simple random sample of 40 jugs were selected and the mean fill volume was found to be 119.5 ounces.
(a) Construct a 94% confidence interval for the true mean fill volume for all jugs of softener.
(b) Conduct a hypothesis test at the 6% level of significance to determine whether there is evidence that the true mean fill volume for all jugs of softener differs from 120 ounces.
(c) Interpret the P-value from the test in (b).
(d) Could the interval in (a) have been used to conduct the test in (b)? If no, explain why not. If yes, explain why, and explain what your conclusion would have been and why.