If a manufacturer (the vendee) buys all items of a particular type from a particular vendor, the manufacturer is practicing sole sourcing (Schonberger and Knod, Operations Management, 2001). As part of a sole-sourcing arrangement, a vendor agrees to periodically supply its vendee with sample data from its production process. The vendee uses the data to investigate whether the mean length of rods produced by the vendor's production process is truly 5.0 millimeters (mm) or more, as claimed by the vendor and desired by the vendee.
a. If the production process has a standard deviation of .01 mm, the vendor supplies n = 100 items to the vendee, and the vendee uses α = .05 in testing H0: µ = 5.0 mm against Ha: µ < 5.0 mm, what is the probability that the vendee's test will fail to reject the null hypothesis when in fact µ = 4.9975 mm? What is the name given to this type of error?
b. Refer to part a. What is the probability that the vendee's test will reject the null hypothesis when in fact µ = 5.0? What is the name given to this type of error?
c. What is the power of the test to detect a departure of .0025 mm below the specified mean rod length of 5.0 mm?