Q. A process that cuts length of metal with high precision aims to produce metal rods with length of 850 millimeters (mm). Management at the factory is concerned that after an adjustment to the machine the mean length of the rods being produced is less than the required 850 mm. The production line manager tasked with investigating the issue finds that a (random) sample of 15 rods yielded a mean length of 847 mm and a sample standard deviation of 3 mm.

(i) Explain briefly whether the information from the sample would prompt the production line manager to continue the investigation.

(ii) State the null and alternate hypotheses for this situation.

(iii) Test the hypothesis from the answer above using a 5% level of significance. What would be the excel output, the rejection criterion, relevant numbers from the output, the test result and a conclusion in terms of the original problem.