An industrial manufacturing facility produces metal L-brackets by bending a piece of metal, then drilling holes into the bent piece. The diameter of each hole should be 8 millimeters, but minor difficulties with the drill can cause this to change. When the drill is working properly, the actual diameter of the drilled holes follows a normal distribution with mean 8 mm and standard deviation 0.5 mm. If the drill is not working properly, the mean could be something different, but we will assume that the standard deviation does not change. The quality control department at the facility routinely selects a random sample L-brackets and measures the diameters of 16 holes. If there is evidence that the mean diameter has shifted from 8 mm (either higher or lower), then production is suspended until the drill can be re-calibrated. The last sample of L-brackets produced mean diameter 8.1 mm. We want to conduct a hypothesis test to determine if this is convincing evidence that the production should be suspended. Suppose that mu is the true mean diameter of the holes that have been most recently drilled.

Question 1: What are the null and alternative hypotheses that should be tested?

Question 2: What is the standardized value of the test statistic?

Question 3: Complete this sentence: At significance level 0.05, we reject H0 if ________.

Question 4: Do we reject the null hypothesis?

Question 5: Based on this hypothesis test, can we conclude that the mean diameter is different than 8 mm?

Question 6: Should the p-value for this test be greater than or less than the significance level? Question 7: Calculate the p-value for this test.