Runger and Pignatiello (1991) consider a plastic injection molding process for a part with a target critical width dimension of 100 and historic standard of 8. Periodically, clogs form in one of the feeder lines, causing the mean width to change. As a result, the operator periodically takes random samples of size four.
(a) A recent sample yielded a sample mean of 101.4. Conduct a hypothesis test to determine whether the mean width has increased. Use a 0.01 significance level.
(b) Find the p-value associated with the test in part (a).
(c) Construct a 99% confidence interval for this situation. Use this interval to determine whether the mean width has changed.
(d) Find the power of test to detect a change in the true mean width to 102.
(e) Find the sample size required to achieve a power of 0.8 when the true mean is 102.