A can of soda is labeled as containing 12 fluid ounces. The quality control manager wants to verify that the filling machine is neither over-filling nor under-filling the cans.
(a) Determine the null and alternative hypotheses that would be used to determine if the filling machine is calibrated correctly.
(b) The quality control manager obtains a sample of 75 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test.
(c) Suppose, in fact, the machine is not out of calibration. Has a Type I or Type II error been made?
(d) Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of significance would you recommend the quality control manager use? Explain.