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
(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
(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
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