Need some questions answered from INTRO TO STATS

Your final exam will be a combination of multiple choice problems and two case studies (one for means, one for proportions) that will put together most of the concepts you have learned up to this point. The following is an example of a case study similar to the one you will be presented.

The Scenario: The production line manager at a factory which produces PVC-Pipe fittings needs to run a quality check on the machine producing elbow fittings for ½” PVC piping. The elbow fittings are supposed to be produced with an average mass of 60g. If the machine is producing lighter fittings it could compromise the integrity of the product, but if the machine is producing heavier fittings there is likely waste occurring.

The Sampling: To test if the machine is calibrated correctly, the manager randomly selects 12 PVC fittings off the production line, with the following results:

1.) Calculate the mean and standard deviation of the mass of the PVC elbows.

2.) As the manager, what would be the appropriate hypothesis test to perform in this scenario? (State the formal hypothesis test using )

3.) Describe what a Type I and Type II error would entail in this scenario, and what the consequences of making each one would be.

4.) Based on your answer in part (3.), which type of error (Type I/Type II) would you rather commit? Based on this, would you test this hypothesis at the, or the level?

5.) Based on the -level you chose in part (4.), calculate a Confidence Interval for the true mean mass of the elbows being produced.

6.) Test the hypothesis from part (2.) at the -level you chose in part (4.).

7.) What is the approximate p-value of your test in part (6.)?

8.) Based on your above results in parts (5.), (6.), and (7.), should the manager be concerned about the calibration of the machine? Be sure to justify your decision using the results from above.